#VLJUBCOIFSIBLLTBLMESWF\":%*/:\":*/-\"3*OBBJUUJSTBZMZBTBOOIÐLÐNMFSJOF HËSFLJUBCOEÐ[FOJ NFUOJ TPSVWFõFLJMMFSJLTNFOEFPMTBIJ¿CJSõFLJMEFBMOQZBZNMBOB- NB[ GPUPLPQJZBEBCBõLBCJSUFLOJLMF¿PóBMUMBNB[ :BZO4PSVNMVTV $BO5&,÷/&- :BZO&EJUÌSÑ #JMJNTFM÷ODFMFNF ÷MIBO#&:\";5\"õ %J[HJ–(SBGJL5BTBSN *4#//P .VTUBGB:·$& :BZOD4FSUJGJLB/P #BTN:FSJ \"ZEO:BZOMBS%J[HJ#JSJNJ ÷MFUJöJN &SUFN#BTN:BZO-UEõUJr \":%*/:\":*/-\"3* JOGP!BZEJOZBZJOMBSJDPNUS 5FMr 'BLT 0533 051 86 17 aydinyayinlari aydinyayinlari * www.aydinyayinlari.com.tr %¸O¾P.DSDáñ·/÷7&34÷5&:&)\";*3-*, ÜNİVERSİTEYE HAZIRLIK 3. MODÜL GEOMETRİ Alt bölümlerin Karma Testler ÇOKGENLER VE DÖRTGENLER EDĜOñNODUñQñL©HULU Çokgenler - Dörtgenler KARMA TEST - 4 1. D ³ Çokgenler t 2 C 4. D C G ³ Dörtgenler t 10 F Modülün sonunda tüm alt bölümleri A3 E 2B A EB L©HUHQNDUPDWHVWOHU \\HUDOñU ³ Yamuk t 18 \"#$% CJS FõLFOBS EËSUHFO [DB] LËõFHFO [DE] ABCD paralelkenar, m ( % ) = 90° DEG | | | |B¿PSUBZ, AE = 3 br, EB = 2 br % % :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCS2 dir? EDF FDG | | | |mak ma k, = AE = EB ³ Paralelkenar t 34 | | | | | | | | | |EF = 3 br, BG = GC , ED + DG = 16 br A) 35 B) 25 2 80 2 C) :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- 9 karedir? ³ Eşkenar Dörtgen t 48 6ñQñIð©LðĜOH\\LĜ D) 50 100 2 ³ Dikdörtgen t 55 E) www.aydinyayinlari.com.tr ·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER 9 A) 40 B) 48 C) 56 D) 64 E) 72 ³ Kare t 67 ÇOKGENLER 2. ôFLJMEFLJ\"#$%EJLEËSUHFOJFõUVóMBEBOPMVõVZPS ÖRNEK 1 DC TANIM ³ Deltoid t 80 ,FOBS TBZT FO B[ п PMBO LBQBM HFPNFUSJL OLFOBSMCJSLPOWFLTÀPLHFOJOCJSLÌöFTJOEFOLÌ- 5. D 10 C õFLJMMFSF çokgen EFOJS¥PLHFOMFSLFOBSTBZ- öFHFO ÀJ[JMFCJMJZPSTB CV ÀPLHFOJO LÌöFHFO TBZT LBÀUS %XE¸O¾PGHNL¸UQHN MBSOBHËSFBEMBOESMSMBS¶¿HFO EËSUHFO CFõ- VRUXODUñQ©¸]¾POHULQH 6 ³ Karma TestleHFrOHtJCJ 86 n - 3 =j n =PMVS AB ¥PLHFOJOJ¿CËMHFTJOEFBMOBOIFSIBOHJJLJOPL- ,ÌöFHFOTBZT= n.^ n - 3 h 9.6 Çevre ( ABCD ) = 92 br dir. <HQL1HVLO6RUXODU = = 27 EJS A EB ³ Yeni Nesil Sorular t 94UBZCJSMFõUJSFOEPóSVQBS¿BT ¿PLHFOJOJ¿JOEF 22 0RG¾O¾QJHQHOLQGH\\RUXP LBMZPSTBCV¿PLHFOEöCÑLFZ LPOWFLT ÀPL- \\DSPDDQDOL]HWPHYE genPMBSBLBEMBOESMS,POWFLTPMNBZBO¿PL- :VLBSEBLJ WFSJMFSF HÌSF Fö EJLEÌSUHFOMFSEFO <(1m1(6m/6258/$5ôFLJMEF[DC] ZBSN¿FNCFSJO¿BQ EHFHULOHUL¸O©HQNXUJXOX biSJOJOÀFWSFTJLBÀCJSJNÇEoJkSgenler - Dörtgenler VRUXODUD\\HUYHULOPLĜWLU $\\UñFDPRG¾OVRQXQGD HFOJTFJÀCÑLFZ LPOLBW ¿PLHFOõFLMJOEFBE- | | | |1C.) WDPDPñ\\HQLQHVLOVRUXODUGDQ MBOESMS DNñOOñWDKWDX\\JXODPDVñQGDQ A) 24 B) 28 3\"2MQFSEDÐ)[3H6ÐOBMEUH) F4O0õFLMJOEFLJNBTBAOBOCD¿FpWaSFraTlJeOlJk enar, 3D.C = 10 br, AD = 6 br ROXĜDQWHVWOHUEXOXQXU 3. D \"#$%EJLZBNVóVCFMJSUJMFOZËOEF\"#LFOBSUBCB- IFTBQMBNBLJ¿JOCJSCJSJOFEJLUBIUBZ#VõOFLBJMHEÌFLSFJ H\"J- \"#$% LBOÀBCEJSFJNóFLDBFSLFECJ¿SJNEFEËOEÐSÐMÐZPS bi birbirine çiviliyor. ÖRNEK 2 C ABCD kareA A) 40 B) 45 C) 48 D) 50B E) 54 C B 1 ,ÌöFHFO TBZT LFOBS TBZTOO LBU PMBO ÀPLHF- |EF| = |BF| XODĜDELOLUVLQL]OJO CJSLÌöFTJOEFOLBÀLÌöFHFOÀJ[JMFCJMJS K ¦PLHFOJOLFOBSTBZTOPMTVO E Konveks çokgen Konkav çokgen n^ n - 3 h F 6. ,FOBSCV[VOMVLMBSCSWFCSPMBOCJSEJLEËSUHFO = 5n CJ¿JNJOEFLJCJSLBóUIFSIBOHJCJSLËõFHFOJOEFOCÐ- D 2 A n - 3 = 10 A FB LÐMFSFL JLJZF LBUMBOZPS WF UFL LBU LBMBO LTNMBS n =UÑS | | | | | |L LFTJMJZPSWFLBóUUFLSBSB¿MCZDPS=CS AD =CSWF AB = 16 br ol- #JSLÌöFEFOÀJ[JMFOLÌöFHFOTBZT :VLBSEBLJWFSJMFSFHÌSF m ( A%DF ) kaç derece- %öCÑLFZ ,POWFLT ¦PLHFOJO²[FMMJLMFSJ n - 3 =EVS 0MVöBOöFLMJOBMBOLBÀCEJVSJôNVLOBBSFHEÌJSSF $OPLUBTJMFZBNVôVOEÌOEÑSÑM- NFTJTPOVDVPMVöBO$OJOCVMVOEVôVZFOJOPL- 9 #VOEBO TPOSB ÀPLHFO EFOJMEJôJOEF EõCÑLFZ $OW%¸O¾P7HVWOHUL dir? E D 75 C) 7UB7BSBDT)OE7B9LJVE[B)LM8L1LBÀCJSJNEJS ÀPLHFOBOMBõMNBMES A) Her alt bölümün B) 38 22 2 A) 10 B) 15 C) 2'0,LBDMB)T3O0OCPEZV) 40CS ,-LBMBTOOCPZ2VCSWF A) 20 2 B) 12 5 C) 8 10 7$1,0%m/*m TEST - 31 -$LBMBTOOCPZVCSEJS #JS ¿PLHFOJO BSEõL, PBMSNFBZBO IFSIBOHJ JLJ LË- %m/*m \"#$%LBSF 1. E 2. C 3#.VDOBHÌSF NBTBOOÀFWS8F9TJLBÀCJSJNEJS 4. D 5. C 6. A D) 10 6 E) 24 õFTJOJCJSMFõUJSFO1E.PóSVDQBS¿BTOBLÌöFHFCO de- m (C%EB) = m (C%BE) OJS \"#$%LBSF A1 4. A2 C A) 42 B) 45 C) 48 D) 51 E) 58 4. ôFLJM * EF WFSJMFO \"#$% QBSBMFMLFOBS õFLMJOEFLJ % # &EPóSVTBM 1 E LVNBõQBS¿BT[BD] boyunca kesiliyor. A BA B A1 A2 |DB| = |CE| D2 * LËõFHFO // A5 2. \"õBóEB WFSJMFO EJLEËSUHFOMFS õFLJMEFLJ HJCJ LFTJM- NJõUJS // A3 * 3 LËõFHFO An A3 DC DB ôFLJM* AB A4 E OLFOBSM¿PLHFOJOCJSLAËõFTJOEFOHF¿FOLËõBF- VRQXQGDRE¸O¾POHLOJLOL ** WHVWOHU\\HUDOñU ** :VLBSEBLJ WFSJMFSF HÌSF m (C%ED) LBÀHB EFZFOSSMFSFSD¿FP-LHFOJ O-: VULBBOSFEÐB¿LHJFWOFTSJFMFMSCFËHMHÌFSZFF m (D%EB)LBÀEFSFDFEJS OLFOBSMCJS¿PLHFOJOCJSLËõFTJOEFO O- DC UBOFLËõFHFO¿J[JMJS EJS #VOFEFOMFJ¿B¿MBSO\"O ËM¿ ÐMFSJUP#Q MBN $ % & OLFOBSMCJS¿PLHFOJ\"O UPQMBNLË#õ FHFOTBZ$T % &O - EJS %BIBTPOSB*QBS¿B\"OPLUBT$OPLUBTOB%OPL- n^ n - 3 h O LFOBSM CJS ¿PLHFOJO Eõ B¿MBSOO ËM¿ÐMFSJ UBT#OPLUBTOBLBSõMLHFMFDFLõFLJMEFEJLJMJQ UBOFEJS *** &#%$EËSUHFOJôFLJM**EFLJHJCJFMEFFEJMJZPS UPQMBNEJS 2 B 2. \"#$%LBSF \"#(FõLFOBSпHFOWF\"(&'FõLFOBS EËSUHFOEJS D C \"#$%LBSF 2 1. 27 2. 10 $ & 'EPóSVTBM E C m ( B%AE ) = % :VLBSEBLJ WFSJMFSF HÌSF DJTJNMFSJO ÀFWSFMFSJ DC D m ( ECB ) OBTMEFôJöJS G F I II III ôFLJM** E F AB A) \"[BMS Artar Artar B) \"[BMS %FóJõNF[ Artar E C) Artar %FóJõNF[ Artar | | | |% D) Artar Artar \"[BMS E) Artar Artar Artar m ( DCA ) = 120°, DC = 10 br, BC = 6 br AB % | | :VLBSEBLJWFSJMFSFHÌSF BD kaç birimdir? CEB % :VLBSEBLJ WFSJMFSF HÌSF m ( ) LBÀ EFSFDF- EFD :VLBSEBLJWFSJMFSFHÌSF m ( ) LBÀEFSFDF- EJS A) 12 B) 14 C) 15 D) 16 E) 18 EJS \" # $ % & 1. D 2. D 95 3. A 4. B \" # $ % & 3. A B \"#$%LBSF D C \"#$%LBSF D F \" ' $ & EPóSVTBM K \" . , $ C EPóSVTBM |CE| = |AD| |DE| = |EF| L % = 28° M m ( KBC ) 28° % m ( LBA ) = 17° E 17° AB :VLBSEBLJ WFSJMFSF HÌSF m (A%FD) LBÀ EFSFDF- EJS :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDF- KLB EJS \" # $ \" # $ % & % & 1. D 2. \" 3. \" 4. C B D
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·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÇOKGENLER TANIM ÖRNEK 1 ,FOBS TBZT FO B[ п PMBO LBQBM HFPNFUSJL OLFOBSMCJSLPOWFLTÀPLHFOJOCJSLÌöFTJOEFOLÌ- õFLJMMFSF çokgen EFOJS¥PLHFOMFSLFOBSTBZ- öFHFO ÀJ[JMFCJMJZPSTB CV ÀPLHFOJO LÌöFHFO TBZT MBSOBHËSFBEMBOESMSMBS¶¿HFO EËSUHFO CFõ- LBÀUS HFOHJCJ n - 3 =j n =PMVS ¥PLHFOJOJ¿CËMHFTJOEFBMOBOIFSIBOHJJLJOPL- UBZ CJSMFõUJSFO EPóSV QBS¿BT ¿PLHFOJO J¿JOEF ,ÌöFHFOTBZT= n.^ n - 3 h 9.6 LBMZPSTBCV¿PLHFOEöCÑLFZ LPOWFLT ÀPL- = = 27 EJS genPMBSBLBEMBOESMS,POWFLTPMNBZBO¿PL- 22 HFOJTFJÀCÑLFZ LPOLBW ¿PLHFOõFLMJOEFBE- MBOESMS Konveks çokgen Konkav çokgen ÖRNEK 2 %öCÑLFZ ,POWFLT ¦PLHFOJO²[FMMJLMFSJ ,ÌöFHFO TBZT LFOBS TBZTOO LBU PMBO ÀPLHF- OJO CJSLÌöFTJOEFOLBÀLÌöFHFOÀJ[JMFCJMJS 9 #VOEBO TPOSB ÀPLHFO EFOJMEJôJOEF EõCÑLFZ ÀPLHFOBOMBõMNBMES ¦PLHFOJOLFOBSTBZTOPMTVO n^ n - 3 h = 5n 2 n - 3 = 10 n =UÑS #JSLÌöFEFOÀJ[JMFOLÌöFHFOTBZT n - 3 =EVS 7$1,0%m/*m %m/*m #JS ¿PLHFOJO BSEõL PMNBZBO IFSIBOHJ JLJ LË- A5 A1 A2 õFTJOJCJSMFõUJSFOEPóSVQBS¿BTOBLÌöFHFO de- 1 OJS 2 3 A3 A1 A2 LËõFHFO A3 LËõFHFO An OLFOBSMCJS¿PLHFOJOCJSLËõFTJOEFO O- A4 UBOFLËõFHFO¿J[JMJS OLFOBSM¿PLHFOJOCJSLËõFTJOEFOHF¿FOLËõF- OLFOBSMCJS¿PLHFOJOUPQMBNLËõFHFOTBZT HFOMFS¿PLHFOJ O- UBOFпHFOTFMCËMHFZF n^ n - 3 h BZSS UBOFEJS 2 #VOFEFOMFJ¿B¿MBSOOËM¿ÐMFSJUPQMBN O- EJS O LFOBSM CJS ¿PLHFOJO Eõ B¿MBSOO ËM¿ÐMFSJ UPQMBNEJS 2 1. 27 2. 10
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 %Ñ[HÑO¦PLHFO 7$1,0%m/*m ÷À BÀMBSOO ÌMÀÑMFSJ PSUBL GBSL PMBO CJS ÌSÑOUÑ 5ÐNLFOBSV[VOMVLMBSWFB¿MBSOOËM¿ÐMFSJFõJU PMVöUVSBOBMUHFOJOFOCÑZÑLEöBÀTOOÌMÀÑTÑLBÀ PMBO¿PLHFOFEÑ[HÑOÀPLHFOEFOJS EFSFDFEJS A1 ¦PLHFOJOFOLÑÀÑLJÀBÀTOOÌMÀÑTÑYPMTVO O- = - =EJS A2 Y+ Y+ + Y+ + Y+ + Y+ + Y+ = Y+= A3 A8 Y= Y=EJS A4 A7 &OCÑZÑLEöBÀ=- A5 A6 =CVMVOVS OLFOBSMEÐ[HÐO¿PLHFOJOCJSEõB¿TOOËM¿Ð- TÐ 360° EJS n OLFOBSMCJSEÐ[HÐO¿PLHFOJOCJSJ¿B¿TOOËM- ¿ÐTÐ180° - 360° n ÖRNEK 4 ÖRNEK 5 ÷LJÀPLHFOJOLFOBSTBZMBSOOPSBOWFLÌöFHFOTB- #JS JÀ BÀTOO ÌMÀÑTÑ CJS Eö BÀTOO ÌMÀÑTÑOÑO ZMBSPSBOPMEVôVOBHÌSF CVÀPLHFOMFSJOJÀBÀ- LBUOBFöJUPMBOEÑ[HÑOÀPLHFOLBÀLFOBSMES MBSOOÌMÀÑMFSJUPQMBNLBÀEFSFDFEJS %Ñ[HÑOÀPLHFOJOCJSEöBÀTOOÌMÀÑTÑaPMTVO 0IBMEFJÀBÀTOOÌMÀÑTÑaPMVS a+ a=j a= 360° n = & n = 18 CVMVOVS 20° ¦PLHFOMFSEFOCJSJOJOLÌöFHFOTBZTOJTFEJôFSJOJOO ÖRNEK 6 EJS,ÌöFHFOTBZMBSPSBOJTF D \"#$%&EÐ[HÐO 3n.^ 3n - 3 h 9.^ n - 1 h CFõHFO 2 = 18 & n-3 = 18 n.^ n - 3 h E C \"#'FõLFOBSпHFO 2 F 36° j n - 1 = 2n - 60° j n =PMVS // 48° 36° 60° A // B // // ¦PLHFOMFSJOJÀBÀMBSOOÌMÀÑMFSJUPQMBN O- + O- =+= CVMVOVS :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS FAC %Ñ[HÑOCFöHFOEF m (XB) = 108°EJS\"#$JLJ[LFOBSÑÀ- HFOJOEF m ( C%AB ) = 36°PMVS \"'#FöLFOBSÑÀFOJOEF m ( F%AC ) = 60° - 36° =PMVS 3. 4. 3 24
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 7 ÖRNEK 9 ,FOBS TBZMBS UPQMBN PMBO JLJ EÑ[HÑO ÀPLHFOJO B C \"#$%&EÐ[HÐOCFõHFO Eö BÀMBSOO ÌMÀÑMFSJ PSBO PMEVôVOB HÌSF LFOBS 54° 54° TBZTB[PMBOÀPLHFOJOLBÀLÌöFTJWBSES |EF| = |DF| 72° |BG| = |CG| G ¦PLHFOMFSJOLFOBSTBZMBSNWFOPMTVO AD // %öBÀMBSOOÌMÀÑMFSJPSBOJTF 360° 360° n // F : = 5 & = 5 & n = 5m olur. mn m E N+ n =jN= :VLBSEBLJWFSJMFSFHÌSF m ( B%GC )LBÀEFSFDFEJS jN=CVMVOVS N=PMEVôVJÀJOLÌöFTJWBSES [#'] #BÀTOOBÀPSUBZPMBDBôOEBO % m ( CBF ) = 54° EJS ÖRNEK 8 #($JLJ[LFOBSÑÀHFOJOEF m ( % ) = 180° - ^ 54° + 54° h = 72° CVMVOVS BGC B C \"#$%&EÐ[HÐO aa aa ¿PLHFO A D [BM]WF[CM]B¿PSUBZ %m/*m 40° % m( BMC ) = 40° AB M :VLBSEBLJWFSJMFSFHÌSF EÑ[HÑOÀPLHFOLBÀLFOBS- F C MES 2a +=j a =EJS #JSJÀBÀa = CJSEöBÀ -=EJS ED ,FOBSTBZT= 360° = 9 CVMVOVS. \"#$%&' EÐ[HÐO BMUHFO JTF [ AD ] TJNFUSJ FL- 40° | | | |seOJWF AD = AB EJS %m/*m ÖRNEK 10 B C A 12 B // \"#$%&'EÐ[HÐO F // BMUHFO D | |5k F C AB =CS A |BK| = 5 |EK| kK ED E | |:VLBSEBLJWFSJMFSFHÌSF EK LBÀCJSJNEJS \"#$%&EÐ[HÐOCFõHFOJOEF[ AF ]OOB¿PSUBZ L= 12.2 j k =CSCVMVOVS LFOBSPSUBZ WF ZÐLTFLMJL PMEVóV EVSVNMBSOEBO FOB[CJSJCJMJOJSTFEJóFSMFSJTËZMFOFCJMJS 7. 3 9 4 9. 72 10. 4
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m ÖRNEK 13 \"#$%&'EÐ[HÐO ¿PLHFO A2 A3 K A4 [FK] a [AK] = {K} 36° A1 m ( F%KA ) = 36° A5 2a + 36° M An D aaC OLFOBSMCJSEÐ[HÐO¿PLHFOEF ¿FWSFM¿FNCFS ¿J[JMEJóJ [BNBO CÐUÐO LJSJõMFS FõJU PMBDBóOEBO aa IFSCJSZBZOËM¿ÐTÐ 360° EJS EB n FA ÖRNEK 11 :VLBSEBLJWFSJMFSFHÌSF CVÀPLHFOLBÀLFOBSMES CD \"#$%&' EÐ[HÐO #JSEöBÀOOÌMÀÑTÑaPMTVO.%$ÑÀHFOJOEF a + a + a + = B a G 22,5° a E ¿PLHFO 157,5° a a = % 360° F m( BGF ) = 157, 5° = 36° j n =CVMVOVS A n . ÖRNEK 14 :VLBSEBLJWFSJMFSFHÌSF ÀPLHFOLBÀLFOBSMES C 20 40 B :BOEB CJS FWJO CBOZPTV- OVO [FNJOJOEF CVMVOBO ¦FNCFSÌ[FMMJôJOEFO BÀTHÌSEÑôÑZBZMBSOUPQ- 20 3 EÐ[HÐOBMUHFOõFLMJOEFLJ MBNMBSOOZBSTES D GBZBOTMBS HËTUFSJMNJõUJS 3a )FSCJSGBZBOTOCJSLFOBS 40 3 30° V[VOMVóVDNEJS = 22, 5° & a = 15° 2 360° n = 15° j n =CVMVOVS 40 3 ÖRNEK 12 A #JSLºóEB\"#$%&'EÐ[HÐOBMUHFOJOJ¿J[JOJ[%BIBTPO- :VLBSEBLJWFSJMFSFHÌSF \"JMF#OPLUBMBSBSBTOBÀF- LJMFOHFSHJOUFMJOV[VOMVôVLBÀTBOUJNFUSFEJS ra [ AD ]EPóSVQBS¿BTO¿J[JQ [ AD ]Ð[FSJOEF(OPLUB- C 60 B sBMO[ 30° % 20 3 1JTBHPSUFPSFNJOEFO 60° 40 3 Y2 = ^ 100 3 h2 +2 m ( AGF ) = 45°WF FG = 4 6 br PMEVôVOBHÌSF çJ[- Y2 = D EJôJOJ[EÑ[HÑOBMUHFOJOÀFWSFTJLBÀCJSJNEJS x = 40 21 DNCVMVOVS A B '()ÑÀHFOJOEF 8 60° 4 | |') = 4 3 CS 43 H C \"')ÑÀHFOJOEF 30° | |\"' =CS x F 45° 45° G ¦ \"#$%&' ==CS 80 3 CVMVOVS 46 ED A 11. 24 12. 13. 10 14. 40 21
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 15 ÖRNEK 17 AF B ABCDE EÐ[HÐOCFõHFO A B \"#$%&EÐ[HÐO [ DF ] m [AB ] CFõHFO |DG | |= GC| // | |EH =CS G \" & 'EPóSVTBM E8 H C 54° // |BG| = |GC| 4k Gk E 54° | | | |C EF = EH 3k 3k k D D | |FG =CS H | |:VLBSEBLJWFSJMFSFHÌSF () LBÀCJSJNEJS F &%(ÑÀHFOJOEFJÀBÀPSUBZUFPSFNJOEFO | |:VLBSEBLJWFSJMFSFHÌSF ') LBÀCJSJNEJS 4k 3k j |)(| =CSCVMVOVS &'(ÑÀHFOJOEFEöBÀPSUBZUFPSFNJOEFO = 8 HG k HG 1 HG = &= j |)(| = CSEJS 3k GF 3 24 |')| = 24 -=CSCVMVOVS ÖRNEK 18 ÖRNEK 16 %Ð[HÐO BMUHFO õFLMJOEFLJ LVNBõ QBS¿BT LFOBSMBSOO пUFCJSJOEFOOPLUBMBSBMOBSBLCFMJSUJMFOZËOMFSEFLBUJ[- AB A#$%&'EÐ[HÐOBMUHFO MFSJ CJSCJSJOF QBSBMFM PMBDBL õFLJMEF LBUMBOBSBL ôFLJM ** EFLJLVNBõQBS¿BTFMEFFEJMJZPS [ BG ] m[GH] 6 [GH] m [HE] AB G 15 | |C K MK M 30 EH =CS F 3 F CF C P | |BG =CS . H | |AF =CS NP NP 3 ED ôFLJM** x ôFLJM* ED | |:VLBSEBLJWFSJMFSFHÌSF () LBÀCJSJNEJS #BöMBOHÀUBLJ LVNBö QBSÀBTOO CJS LFOBS N PM- EVôVOB HÌSF õFLJM ** EF LVNBöO NBWJ HÌSÑOFO | BE | = 2 |\"#| ==CSEJS CÌMHFTJOJOBMBOLBÀNFUSFLBSFEJS [BP] m [PE]PMBDBLöFLJMEF[GP]WF[PE]OÀJ[FMJN A 12 B ^ 12 + 16 h.2 3 4 A^ ABMK h = | PE | = |()| =YCS 4 23 16 M | PG | = |&)| =CSPMVS1#&EJLÑÀHFOJOEF K2 12 8 2 8 = 28 3 Y2 + 92= 302 j x = 3 91 CSCVMVOVS C 60° 12 2 8 F A^ ABCDEF h = f 12 3 p.6 8 P 4 4 N D = 216 3 4 E 12 5BSBMBMBO= 216 3 - 112 3 = 104 3 m2 CVMVOVS 3 91 17. 104 3
¦PLHFOMFS TEST - 1 1. ,ÌöFHFOTBZTLFOBSTBZTOOLBUPMBOEö- D CÑLFZ ÀPLHFOJO JÀ BÀMBSOO ÌMÀÑMFSJ UPQMBN C LBÀEFSFDFEJS E A # $ B & % F 2. EFOLпÐLJ¿B¿TPMNBZBOCJSBMUHFOJO пJ¿ A H B¿TOOËM¿ÐMFSJUPQMBNEJS G #VOBHÌSF EJôFSÑÀBÀZBLPNöVPMBOEöBÀ- [ AG ]EõOEBEJóFSLFOBSV[VOMVLMBSFõJUPMBOZFEJ- MBSEBOFOLÑÀÑôÑFOB[LBÀEFSFDFPMBCJMJS | |HFOEF AG =CS \" # $ % & 'WF(OPLUBMBS )OPLUBTOBFõJUV[BLMLUBES #VOBHÌSF ZFEJHFOJOBMBOLBÀCJSJNLBSFEJS \" # $ % & \" # $ % & 3. #JS¿PLHFOJOEËSUJ¿B¿TOOËM¿ÐMFSJFõJUPMVQ EJóFS #JSLFOBSOOV[VOMVóVNPMBOõFLJMEFLJ J¿B¿MBSOOËM¿ÐMFSJUPQMBNEJS \"#$%&'( EÐ[HÐO ZFEJHFO õFLMJOEFLJ CJS VDV LB- ZBOO ( LËõFTJOF TBCJUMFOFO N V[VOMVóVOEBLJ #VOB HÌSF FöJU JÀ BÀMBSEBO IFS CJSJ FO B[ LBÀ JQ\"INFUUBSBGOEBOLBZBOOFUSBGOBTBBUZËOÐOEF EFSFDFEJS EËOEÐSÐMFSFLHFSHJOCJSõFLJMEFTBSMODBJQJOEJóFS VDVOVOHFMEJóJTPOOPLUB,PMVZPS \" # $ % & AB C G 4. #JSLPOWFLT¿PLHFOJOLFOBSTBZTLBUOB¿LBS- FD MSTBJ¿B¿MBSOOËM¿ÐMFSJUPQMBN 4 LBULBEBSBSU- E 3 #JSVDV'OPLUBTOBTBCJUMFOFONV[VOMVóVOEB- NBLUBES LJCBõLBCJSJQJ)BTBOLBZBOOLFOBSMBSOBTBBUZË- OÐOÐO UFSTJOF HFSHJO CJS õFLJMEF TBSODB JQJO EJóFS #VOBHÌSF CVÀPLHFOLBÀLFOBSMES VDVOVOHFMEJóJTPOOPLUB.PMVZPS #VOB HÌSF , OPLUBT JMF . OPLUBT BSBTOEBLJ V[BLMLLBÀNFUSFEJS \" # $ % & \" # $ % & 1. D 2. B 3. B 4. $ 7 \" B
TEST - 2 4. ¦PLHFOMFS D 1. \"#$%&'EÐ[HÐOBMUHFOJOJOLFOBSMBSOBEõUBOLB- SFMFSZBQõUSMNõ LBSFMFSJOLËõFMFSJEPóSVQBS¿BMB- SJMFCJSMFõUJSJMFSFLCJSTÐTMFNFZBQMNõUS E FK C A B AB F C \"#$%&EÐ[HÐOCFõHFO \"#'FõLFOBSпHFOEJS :VLBSEBLJWFSJMFSFHÌSF m ( B%FK )LBÀEFSFDFEJS E D \" # $ % & #VOBHÌSF * 4ÐTMFNFTPOVDVPMVõBOõFLJMEÐ[HÐO POJLJHFOEJS D ** 0MVõBOпHFOMFSFõLFOBSпHFOEJS G E *** 4ÐTMFNF TPOVDV PMVõBO õFLMJO BMBO EÐ[HÐO C BMUHFOJOBMBOOOLBUES ZBSHMBSOEBOIBOHJMFSJEPôSVEVS \" :BMO[* # :BMO[** $ * ** F AB % * *** & * ** *** 2. \"#$%&EÐ[HÐOCFõHFO \"#(WF#$'FõLFOBSп- HFOEJS C D :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- B E GFB 135° A F EJS \" # $ % & D E \" # $ % % &WF'CJSEÐ[HÐO¿PLHFOJOBSEõL C F B LËõFMFSJ m ( % ) = 135°EJS G ABF A H :VLBSEBLJ WFSJMFSF HÌSF CV EÑ[HÑO ÀPLHFOJO LFOBSTBZTLBÀUS \" # $ % & 3. #JSLFOBSCJSJNPMBOFöLFOBSÑÀHFOJOJÀJOF \" # $ % & ' (WF)LFOBSMCJSEÐ[HÐO¿PL- HFOJOBSEõLLËõFMFSJEJS ÀJ[JMFCJMFDFL FO CÑZÑL BMBOM EÑ[HÑO BMUHFOJO ÀFWSFTJLBÀCJSJNEJS :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- ACG \" # $ % & EJS \" # $ % & 1. $ 2. D 3. D 4. E B E
¦PLHFOMFS 3. A TEST - 3 1. ôFLJMEF\"#$%&EÐ[HÐOCFõHFOJõFLMJOEFLJCJSCËM- H 6 B4 C D HF WFSJMNJõUJS #V CFõHFOJO \" LËõFTJOEF \"MJ # LË- õFTJOEF #ÐõSB $ LËõFTJOEF $FSFO % LËõFTJOEF E %FSFO &LËõFTJOEF&NSF J¿CËMHFTJOEFLJ'OPLUB- TOEBJTF'BSVLPUVSNBLUBES A B GF E F \"#&'()EÐ[HÐOBMUHFO \" # $EPóSVTBM C D | | | |BC =CS AB =CS :VLBSEBLJWFSJMFSFHÌSF DE PSBOLBÀUS BD A) 1 B) 3 C) 2 D) 5 E) 3 22 \"MJ 'BSVL &NSF WF %FSFOhJO FWMFSJOJO CFMJSMFEJóJ 4. ôFLJM*EFLJLBSUPOEÐ[HÐOCFõHFOõFLMJOEFEJS,BS- EËSUHFOTFM CËMHFOJO BMBO , PMTVO \"MJ %FSFO WF UPO[BD]LËõFHFOJCPZVODBLFTJMFSFLFMEFFEJMFOп- $FSFOhJOFWMFSJOJOCFMJSMFEJóJпHFOTFMCËMHFOJOBMB- O.PMTVO HFO LBSUPO CJSFS LFOBSMBS ¿BLõBDBL õFLJMEF EJóFS #VOBHÌSF ,WF.CÌMHFMFSJOJOCÑZÑLMÑôÑJMF LBSUPOBôFLJM**EFLJHJCJZBQõUSMZPS JMHJMJBöBôEBLJMFSEFOIBOHJTJTÌZMFOFCJMJS A) K > M A B) K = M C) K < M BE D) ,â. ôFLJM* E) 7FSJMFOCJMHJMFSZFUFSMJEFóJMEJS C D 2. E A E FD B ôFLJM** G D A BC C #$%&'EÐ[HÐOCFõHFO [ CA ] a [ DA ] = {A} |BG| = |FG| õFLJM * EFLJ \" OPLUBTOO [$%] LFOBSOB PMBO V[BLMô CS õFLJM ** EFLJ [\"&] WF [BD] EPôSV :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- DAC QBSÀBMBSBSBTOEBLJV[BLMLCSPMEVôVOBHÌ- EJS SF ** öFLJMEF % OPLUBTOO [$&] LFOBSOB PMBO V[BLMôLBÀCJSJNEJS \" # $ % & \" # $ % & 1. \" 2. $ 9 3. E 4. $
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr DÖRTGENLER TANIM ÖRNEK 1 )FSIBOHJ пРEPóSVTBM PMNBZBO EËSU OPLUBZ A B \"#$%EËSUHFO CJSMFõUJSFOEPóSVQBS¿BMBSOOCJSMFõJNJOFEÌSU- 60° 140° genEFOJS E [ DE ]WF[ CE ] B¿PSUBZ m ( D%AB ) = 60° TANIM % = 140° m ( ABC ) A B D C // /% // :VLBSEBLJWFSJMFSFHÌSF m ( DEC )LBÀEFSFDFEJS EF m ( % ) = 60° + 140° = 100° DEC / 2 DC \" # $WF%OPLUBMBSEËSUHFOJOLËõFMFSJ B%AD %m/*m % % % B¿MBSOBEËSUHFOJnJÀBÀMBS A B ABC, BCD, CDA [ AB ] [ AD ] [ BC ] WF [ CD ] EPóSV QBS¿BMBS E F EÌSUHFOJOLFOBSMBS ,PNõVPMNBZBOJLJLFOBSOPSUBOPLUBMBSOCJS- DC MFõUJSFOEPóSVQBS¿BTOBEËSUHFOJOPSUBUBCBO EFOJS [EF]PSUBUBCBOES \"#$%EËSUHFOJOEF[\"'WF[EC]B¿PSUBZPMNBL Ð[FSF %% % m ( ABC ) - m ( ADC ) m ( CEF ) = EJS 2 %m/*m ÖRNEK 2 A B A B \"#$%EËSUHFO 170° E [\"'WF[ CE ] F B¿PSUBZ 70° E % = 70° m ( ADC ) DC % = 170° m ( ABC ) \"#$% EËSUHFOJOEF [AE] WF [BE] B¿PSUBZ PM- DC NBLÐ[FSF :VLBSEBLJWFSJMFSFHÌSF m ( C%EF )LBÀEFSFDFEJS m ( A%EB ) = m ( % ) + m ( % ) % 170° - 70° BCD CDA m ( CEF ) EJS = = 50°CVMVOVS 2 2 10 1. 100 2.
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 3 ÖRNEK 5 A B E \"#%$EËSUHFO A 5B \"#$%EËSUHFO 68 [ CE ]WF[DE] DC [ BD ] m [ AC ] B¿PSUBZ | |AB =CS | |AD =CS % = 40° | |BC =CS m ( CED ) C DF :VLBSEBLJ WFSJMFSF HÌSF m ( % ) + m ( % ) UPQMB- CAB ABD NLBÀEFSFDFEJS | |:VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS 100° % + % ) = 260° 2 +2 =2 + |%$|2 80° m ( CAB ) m ( ABD |%$|2 =j |%$| = 5 3 CSCVMVOVS AB CVMVOVS E 40° C DF ÖRNEK 6 A B \"#$%EËSUHFO aa 160° ÖRNEK 4 [ AF ]WF[ CE ] B¿PSUBZ A B \"#$%EËSUHFO m % ) = 160° ( ABC E % ( ADC ) 70° [ AD ] m [ BD ] 60° 8 m = 40° |AD| = |DC| 40° 5 a+40° b | |EC =CS D b [BD]B¿PSUBZ | |EF =CS F xC D C m ( D%AB ) = 70° | |:VLBSEBLJWFSJMFSFHÌSF '$ LBÀCJSJNEJS :VLBSEBLJWFSJMFSFHÌSF m ( % LBÀEFSFDFEJS 2a + 2b + 200 = BDC) a + b = A B \"#, WF $%, JLJ[LFOBS Y2 =2 +2 -DPT DPTUFPSFNJ 70° 20° ÑÀHFO 1 20° =+- 50° % = 50° 2 m ( BDC ) Y2 = 49 jY=CVMVOVS D 40° 70° C 70° %m/*m K %m/*m AB E A B a E DC \"#$%EËSUHFOJOEF[AC]WF[BD]LËõFHFO DC % = a m ( DEC ) [ BD ] m [ AC ]JTF A (ABCD) = 1 . BD . AC . sin aES | | | | | | | |AB 2 + DC 2 = AD 2 + BC 2 EJS 2 3. 4. 11 5 3 7
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 7 %m/*m A B H E A 4 B 5 E5 D a4 F 38 C G 54 D C \"#$%EËSUHFOJOEF & ' (WF)LFOBSMBSOPS- UBOPLUBMBSJTF ABCD EËSUHFO [ DB ] a [ AC ] = { E } &'()QBSBMFMLFOBSES | | | | | | | | | |DE = EB = DC =CS AE =CS EC =CS [ BD ] m [ AC ]JTF&'()EJLEËSUHFOEJS :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS | | | |BD = AC JTF&'()FõLFOBSEËSUHFOEJS %LÌöFTJOEFO[\"$]ZFEJLNFJOFMJN 3 | | | |[ BD ] m [ AC ]WF BD = AC JTF&'()LBSFEJS sin a = PMVS A ( ABCD ) =\" &'() ES 5 13 2 A (ABCD) = 12.10. = 36 br CVMVOVS. 25 && && A^ AEF h + A^ HCG h = A^ FDG h + A^ EBH hEJS %m/*m A B mSPAT S1 S2 \"õBóEB CJS EËSUHFOJO LFOBSMBSOO PSUB OPLUB- S4 E MBSOO CJSMFõUJSJMNFTJ JMF PMVõUVSVMBO EËSUHFOJO S3 CJSQBSBMFMLFOBSPMEVóVJTQBUMBONõUS B DC E A \"#$%EËSUHFOJOEF [ AC ] a [ BD ] = {E}PMNBL H Ð[FSF S143 = S24EJS F ÖRNEK 8 B \"#$%EËSUHFO C A G A [ AC ] a [ BD ] = { E } D 4 E && | | | | | | | |AE = EB WF BH = HC PMEVóVOEBO\"#$ A^ AED h = 2.A^ BEC h 2A пHFOJOEF[ EH ] // [ AC ]EJS 8 | | | | | | | |AF = FD WF DG = GC PMEVóVOEBO\"%$ DC пHFOJOEF[ FG ] // [ AC ]EJS A^ & h = 2.A^ & h =CS2PMEVôVOBHÌSF A^ & h #VEVSVNEB[ EH ] //[ FG ]PMVS DEC AEB BEC | | | | | | | |AE = EB WF AF = FD PMEVóVOEBO\"#% LBÀCJSJNLBSFEJS пHFOJOEF[EF ] // [ BD ]EJS A^ & h =\"PMTVO A ( A&ED ) = 2A PMVS BEC | | | | | | | |DG = GC WF HC = BH PMEVóVOEBO \"\"=j\"2 =j\"=CS2EJS [ GH ] // [ BD ]EJS & =CS2CVMVOVS #VEVSVNEB [ GH ] // [ EF ]PMVS A^ BEC h 4POPMBSBL [ GH ] // [ EF ]WF[ EH ] // [ FG ]PMEV- óVOEBO&'()QBSBMFMLFOBSES 7. 4 12
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 9 // G // B ÖRNEK 11 \"#$%EËSUHFO ba 2a A D [ AE ] // [ CD ] FH A 2b [ AB ] m [ BC ] A | |AB =CS ab C B A | |BC =CS // B E D EC C \"#$%EËSUHFO (WF&CVMVOEVLMBSLFOBSMBSOPSUBOPL- :VLBSEBLJ WFSJMFSF HÌSF \" \"#&% LBÀ CJSJNLBSF- EJS | | | | | | | | | | | |UBMBS AH = HC DF = FB AD + BC =CS \"&%WF\"&$ÑÀHFOMFSJOJOZÑLTFLMJLMFSJFöJUWFIFSJLJÑÀ- :VLBSEBLJ WFSJMFSF HÌSF &'() EÌSUHFOJOJO ÀFWSFTJ LBÀCJSJNEJS HFOJOUBCBO|\"&|LFOBSPMEVôVOEBO \"#$ÑÀHFOJOEF[(']PSUBUBCBOPMEVôVOEBO|('| =CJTF && |\"%| =CEJS A^ AED h = A^ AEC hEJS #%$ÑÀHFOJOEF['&]PSUBUBCBOPMEVôVOEBO|'&| =BJTF |#$| =BESC+B=CS & \" \"#&% =\"+ B +$= A^ ABC h ¦FWSF ('&) =B+C =CSCVMVOVS A (ABED) = 4.10 = 20CS2CVMVOVS 2 ÖRNEK 10 ÖRNEK 12 A FB \"#$%EËSUHFO E A //E // |AE| = |ED| 10 A 6 B // |DG| = |GC| B A H |AF| = |FB| K / G // [ EF ] m [ EG ] D / | |EF =CS C | |EG =CS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- DC EJS \"#$%EËSUHFO % \" &EPóSVTBM [ BE ] m [ DE ] ) [#$]LFOBSOOPSUBOPLUBTPMTVO | | | |[ AB ] // [ DC ] AD =CS BE =CS & &')(EJLEÌSUHFOPMVS :VLBSEBLJWFSJMFSFHÌSF A^ ABC hLBÀCJSJNLBSFEJS \" &')( ==CS2 \" \"#$% = 2.30 =CS2CVMVOVS \"#$%ZBNVLPMEVôVOEBO \" \"%, =\" #,$ =\"ES & = & = 10.6 = 30 CS2 CVMVOVS A ( ABC ) A ( ABD ) 2 9. 24 10. 13 11. 20 12. 30
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 13 ÖRNEK 15 A B \"#$%EËSUHFO M .N h E [ AC ] m [ BD ] E h \"#$%EËSUHFO FG D C // / | |AC =CS // / | |BD =CS 3 [ AE ]WF[ BE ]B¿PSUBZ |AF| = |FD| h |BG| = |GC| | |AD =CS 5 | |BC =CS D HC AK B :VLBSEBLJWFSJMFSFHÌSF A (BEC) PSBOLBÀUS | |:VLBSEBLJWFSJMFSFHÌSF '( LBÀCJSJNEJS A (ADE) %$ LFOBSOO PSUB OPLUBT PMBDBL öFLJMEF ) OPLUBTO \"&WF#&BÀPSUBZPMEVôVOEBO BMBMN | KE | = | EM | = | EN | =IPMVS [()] // [ BD ]WF[\"$] // [')]PMEVôVOEBO 5.h A (BEC) 2 5 % ) = 90° PMVS m ( FHG = = CVMVOVS A (ADE) 3.h 3 [')]WF[()]PSUBUBCBOPMEVôVOEBO|')| =CSWF |()| =CSPMVS 2 |'(|2 = 32 + 42 j |'(| =CSCVMVOVS ÖRNEK 14 ÖRNEK 16 B \"#$%EËSUHFO A \"#$%EËSUHFO A 4h [ AE ] // [ DC ] 8 A D \"#$FõLFOBSпHFO E A E B | |AE =CS |BE| = |ED| 5-h 5 | | | |BC = DC =CS C | |AC =CS % B m ( BCD ) = 30° 30° B D 10 C :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- EJS EJS A^ ABC h = 8 2 3 B den |%$|ZF%EFO|\"&|ZFEJLMFSJOEJSFMJN 4 = 16 3 2 = A + B br \" \"#$% = A ( & ) + A ( A&ED ) + A ( A%EB ) BCD \" \"#$% = \"+# = 32 3 CVMVOVS 10.5 4. (5 - h) 4.h =+ + 2 22 70 = 2 2 = 35 br bulunur. 13. 14. 14 5 32 3 3
%ÌSUHFOMFS TEST - 4 1. A B \"#$%EËSUHFO 4. A B [ AF ] [ BF ] [ DE ] 60° E WF[ CE ]B¿PSUBZ 5x+5 m ( A%FB ) = 2x D 2x % C m ( DEC ) = 5x + 5° C D F | | | | | |\"#$%EËSUHFO AB = AD = DC :VLBSEBLJWFSJMFSFHÌSF YLBÀEFSFDFEJS m ( B%AD ) = 60° % = 100° \" # $ % & m ( ADC ) :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- DCB EJS \" # $ % & 2. A 3x+30° B 2x+5° C ôFLJM*EFEËSUHFOõFLMJOEFLBSUPOWFSJMNJõUJS AB x D | | | | | | | | \"#%$EËSUHFO AB = AC BD = DC % = 3x + 30° m ( % ) = 2x + 5° DC m ( BAC ) ACD ôFLJM* m ( B%DC ) = x° #V LBSUPO & $% LFOBS Ð[FSJOEF CJS OPLUB PMNBL :VLBSEBLJWFSJMFSFHÌSF YLBÀEFSFDFEJS Ð[FSF #&$ пHFOJ [ BE ] CPZVODB LBUMBOEóO- \" # $ % & | | | |EBôFLJM**EFLJHËSÐOUÐPMVõVZPS AB = BC WF m ( A%BK ) = 70°EJS AB 3. A B \"#$%EËSUHFO 60° 150° [AE]WF[CE] D E B¿PSUBZ % = 60° K m ( ADC ) D % ôFLJM** E m ( AEC ) = 150° C :VLBSEBLJ WFSJMFSF HÌSF % LBÀ EFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( A%KB )LBÀEFSFDF- m ( ABC ) EJS EJS \" # $ % & \" # $ % & 1. B 2. D 3. D 4. $ $
TEST - 5 %ÌSUHFOMFS 1. A \"#$%EËSUHFO 4. A B \"#$%EËSUHFO 6 F B 5 3 [ AC ] a [ BD ] = {F} E C |ED| |= AE| F | | | |BF = FC | |AB =CS D 5 | |D AD = 5 3 CS [ AC ] m [ BD ] C | |E BC =CS | |AC =CS | FE | = | CE | = | ED | | |BD =CS | | :VLBSEBLJWFSJMFSFHÌSF '& LBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS \" # $ % & \" # $ % & 2. B \"#$%EËSUHFO A B \"#$%EËSUHFO 60° C [ AB ] m [ BC ] | |AC =CS A | |BD =CS 2 m ( D%AB ) = 60° DC 60° % ) = 60° m ( ADC :VLBSEBLJ WFSJMFSF HÌSF EÌSUHFOJO CÑUÑO LF- OBSMBSOOPSUBOPLUBMBSCJSMFöUJSJMFSFLPMVöUVSV- D MBOZFOJEÌSUHFOJOÀFWSFTJLBÀCJSJNEJS AD =CS | |10 \" # $ % & | |DC =CS | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS A) 2 3 B) 3 3 C) 4 3 D) 5 3 E) 6 3 3. A \"#$%EËSUHFO ôFLJMEF \"#$% EËSUHFOJ õFLMJOEFLJ UBSMB WFSJMNJõUJS B ¥JGU¿J)BLBOLFOBSMBSOPSUBOPLUBMBSOBLB[LMBS¿B- [ AC ] m [ BD ] LQ CJSCJSJOF EJL JLJ JQ ZBSENZMB UBSMBZ CËMHFMFSF BZSZPS EG |AE| = |ED| A GB E F |BF| = |FC| | |AC =CS DF C | |D C BD =CS | | :VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS | | | |BD =N \"$ =NPMEVôVOBHÌSF )B- LBOhOCVJöJÀJOLBÀNFUSFJQFJIUJZBDWBSES \" # $ % & \" # $ % & 1. B 2. $ 3. B 4. \" D D
%ÌSUHFOMFS TEST - 6 1. A B 4. \"#$%EËSUHFOJõFLMJOEFLJCBI¿FEF%WF$OPLUBMB- 6 SOEBOCVMVOEVLMBSB¿MBSOB¿PSUBZMBSPMBDBLõF- 4E LJMEF¿FLJMFOJQMFS&OPLUBTOEBLFTJõJZPS 8 AB 10 8 43 DC DC | | | | | |\"#$%EËSUHFO BC = EC =CS EB =CS \"WF#OPLUBMBS&JMFCJSMFõUJSJMFSFL \"%&CËMHFTJOF | | | |DE =CS AE =CS QBUBUFT #$&CËMHFTJOFTPóBOFLJMJZPS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS A) 10 55 B) 11 55 C) 12 55 D) 13 55 E) 15 55 | | | |\"% =NWF #$ =NPMEVôVOBHÌSF QBUB- UFTFLJMFOBMBOOTPôBOFLJMFOBMBOBPSBOLBÀ- US 2. C A) 2 C) 4 D) 2 8 E) B B) 1 3 33 4 A 5E 6D \"#$%EËSUHFO [ BA ] m [ AD ] [ BE ] // [ CD ] %ËSUHFOõFLMJOEFLJCBI¿FBõBóEB\"#$%EËSUHFOJ | | | | | |AB =CS AE =CS ED =CS JMFNPEFMMFONJõUJS :VLBSEBLJWFSJMFSFHÌSF \" \"#$& LBÀCJSJNLBSF- AB EJS \" # $ % & 3. D 6 \"#$%EËSUHFO D EC C 8 [ BD ]B¿PSUBZ #BI¿FOJO CJS LTN ZFõJM BMBO CJS LTN UBõMBSEBO AE PMVõNVõUVS #BI¿WBO .FUFIBO ZFõJM BMBO LTNO | |AD =CS TVOJ¿JNJMFZFOJMFNFLJTUJZPS | |DC =CS [AB] // [DC] [BC] m [DC] [BE] // [AD] B & | | | |BC =N DC =N :VLBSEBLJWFSJMFSFHÌSF A^ ABD h PSBOLBÀ- :VLBSEBLJWFSJMFSFHÌSF .FUFIBOhOLBÀN2TV- US A^ ABCD h OJÀJNFJIUJZBDWBSES 1 2 3 1 4 \" # $ % & A) B) C) D) E) 7 7 7 2 7 1. $ 2. $ 3. E 17 4. $ $
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr :\".6, 7$1,0%m/*m %m/*m öLJ LFOBS QBSBMFM PMBO EËSUHFOF ZBNVL EFOJS A c B 1BSBMFM LFOBSMBSB UBCBO EJóFS LFOBSMBSB ZBO E KL LFOBSMBSEFOJS / Yan kenarlar F //A TabanB / // Yan kenarlar Da C D Taban C \"#$%ZBNVóVOEB \"#$%ZBNVóVOEB | | | | | | | |AE = ED WF BF = FC JTF [EF]PSUBUB- r [AB] // [DC] CBOES r m ( D%AB ) + % = 180° EF = AB + DC EJS m ( ADC ) 2 r % + % = 180°EJS EK = LF = c m ( ABC ) m ( DCB ) 2 ÖRNEK 1 EL = KF = a 2 D 5C \"#$%ZBNVL 130° KL = a - c 50° | |DC =CS 2 50° | |BC =CS 4 130° | |AB =CS ÖRNEK 3 50° A A 5 9 K 4B % m ( ADC ) = 130° 6B :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS DCB \"%LFOBSOBQBSBMFMPMBDBLöFLJMEF[$,]EPôSVQBSÀBTOÀJ[FMJN K F E GH $#&JLJ[LFOBSÑÀHFOJPMVöVSm ( D%CB) = 50° + 50° = 100° olur. ÖRNEK 2 D8C D C \"#$%ZBNVL \"#$%ZBNVL [AB] // [DC] [ BD ] a [ AC ] = { K} m n [DE]WF[CE]B¿PSUBZ | | | | | | | | | | | |AE = ED BF = FC AB =CS DC =CS m n | |:VLBSEBLJWFSJMFSFHÌSF () LBÀCJSJNEJS m ( D%AB ) + m ( C%BA ) = 80° 8+6 a x b EF = mn 2 A EB = 7 br :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS #\"%ÑÀHFOJOEF| EG|PSUBUBCBOPMEVôVOEBO| EG | =CS DEC #\"$ÑÀHFOJOEF|)'|PSUBUBCBOPMEVôVOEBO|)'| =CS |()| = |&'| - | EG | - |)'| a + b = N+ a = = 7 - 3 - 3 =CS + 2n + b = N+O + a + b = N+ n = N+ n +Y=jY= 1. 100 2. 40 3. 1
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, %m/*m %m/*m A B A B E DC DC \"#$%JLJ[LFOBSZBNVL \"#$%ZBNVLJTF | | | |[AC] a [BD] = {E}JTF AD = BC |AC|2 + |BD|2 = |BC|2 + |AD|2 |+ AB||DC| |AC| = |BD| |DE| = |EC| |AE| = |EB|EJS ÖRNEK 4 B \"#$%ZBNVL A cB 6 A3 C [ AB ] // [ DC ] DE c FC 4 | |AB =CS a D7 | |AD =CS | |BC =CS | |DC =CS \"#$%JLJ[LFOBSZBNVL [ AE ] m [ DC ]WF | | | |AC + BD =CS | | | |[ BF ] m [ DC ]JTF DE = FC = a - c EJS | | | |:VLBSEBLJWFSJMFSFHÌSF \"$ BD ÀBSQNLBÀCJ- 2 SJNLBSFEJS |\"$|2 + | BD |2 = 42 +2 + 2.3.7 =CS2 ÖRNEK 5 C [ DC ] // [ AB ] |\"$| + | BD | 2 = 2 |\"$|2 + 2 |\"$| . | BD | + | BD |2 = 144 D [ AD ] m [ BD ] 94 + 2 |\"$| . | BD | = 144 3 | | | |4 3 AD = BC =CS |\"$| . | BD | =CS2CVMVOVS | |BD =CS x ÷LJ[LFOBS:BNVL B A 1,8 K x b 5 M 1,8 B 7$1,0%m/*m A b | |:VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS a a [DK] m [\"#]WF[$.] m [\"#]PMBDBLöFLJMEF[DK]WF[$.] D C EPôSVQBSÀBMBSOÀJ[FMJN ²LMJUUFPSFNJOEFO :BO LFOBSMBSOO V[VOMVóV FõJU PMBO ZBNVóB 32 =Y |%$| =- JLJ[LFOBSZBNVLEFOJS Y= CS= CS öLJ[LFOBSZBNVóVOUBCBOB¿MBSFõJUUJS 4. 19
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr %m/*m ÖRNEK 8 AE B D 4C [ DC ] // [ AB ] G 3a 32 | AD | = | BC | 3 // 3 a | |BC = 3 2 CS // 4 3B a | |CD =CS A3 D FC 3.m ( % = % ) DAB ) m ( BCD \"#$%JLJ[LFOBSZBNVL [AB] // [DC] [AC] a [BD] = {G} [AC ] m [ BD ] [EF] m [DC] | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS EF = AB + DC EJS ma % k + ma % k = 180° 2 DCB CBA 4a =j a = |\"#| =CSEJS ÖRNEK 6 AB [ AB ] // [ DC ] ÖRNEK 9 C \"#$%ZBNVL E | AD | = | BC | D // [BD] a [AC] = {E} [AC] a [BD] = { K } [ BD ] m [ AC ] [ AF ] m [ DC ] K |AD| = |BC| 82 DF | | | |C DC - AB =CS 135° | |AF =CS % = 22, 5° m ( BAC ) | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS 22,5° 22,5° | |AC = 8 2 CS A B AB + DC :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS AF = 2 = 16 4JOÑTBMBOGPSNÑMÑOEFO AB + DC = 32 A^ ABCD h = 1 2 .8 2· 2 = 32 2 CS2CVMVOVS DC - AB = 8 ·8 + 22 2 |%$| = |%$| =CS |\"#| =CSCVMVOVS ÖRNEK 7 %JL:BNVL B 7ANnM 5BCBOV[VOMVLMBSCJSJNWFCJSJNPMBOCJSJLJ[LFOBS ZBNVL¿J[JOJ[ A #VZBNVôVOLÌöFHFOMFSJOEFOCJSJOJOV[VOMVôVCJ- [ BA ] m [ AD ] SJNPMEVôVOBHÌSF ZBNVôVOZÑLTFLMJôJLBÀCJSJNEJS [ CD ] m [ AD ] A8B # EFO WF \" EBO EJL JOEJSF- DC MJN 1JTBHPSUFPSFNJOEFO 13 Y2 + 122 = 132 :BO LFOBSMBSOEBO CJSJ BMU UBCBOOB WF ÐTU UB- x CBOOBEJLEVSVNMVPMBOZBNVLMBSBEJLZBNVL Y=CSCVMVOVS EFOJS D4 8 4C 12 7. 20 10 9. 32 2
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 10 B \"#$%EJLZBNVL ÖRNEK 11 B \"#$%EJLZBNVL A [ FB ] m [ BC ] A [ AD ] m [ DC ] F [ DE ] m [ BC ] E [ BD ] m [ AC ] 8 ax | | | |E | |AD =CS k 8 DC = FD D | | | |AB 2 + DC 2 =CS2 2k | |b DE =CS b C C aM D :VLBSEBLJ WFSJMFSF HÌSF ' OPLUBTOO %& LFOBSOB | | | |:VLBSEBLJ WFSJMFSF HÌSF \"# + %$ UPQMBN LBÀ FOLTBV[BLMôLBÀCJSJNEJS CJSJNEJS kx |\"%|2 = |\"#| . |%$| '.%WF%&$ÑÀHFOMFSJCFO[FSMJôJOEFO = = |\"#| . |%$| |\"#| + |%$| 2 = |\"#|2 + 2 |\"#| . |%$| + |%$|2 2k 8 Y=CSCVMVOVS = 272 += 400 %m/*m |\"#| + |%$| =CSCVMVOVS A B E :BNVLUB\"MBO // %m/*m A B DC \"#$%EJLZBNVóVOEB [AC] a [BD] = {E} [ BD ] m [ AC ]JTF | | | | | |AD 2 = AB DC ES DE C \"#$%ZBNVóVOEB [AE] m [DC]PMNBLÐ[FSF mSPAT a AB + DC k AE AB A^ ABCD h = 2 EJS E AB E FD C $ WF % JMF EPóSVTBM PMBDBL õFLJMEF ' OPLUBT DC BMQ[AF] // [BD]PMBDBLõFLJMEF[AF]¿J[FMJN#V EVSVNEB % = 90°PMVS | | | | \"#$%ZBNVóVOEB BE = EC JTF m ( FAC ) \"'$пHFOJOEF±LMJEUFPSFNJOEFO & A^ ABCD h A^ ADE h = EJS | | | | | | | | | |AD 2 = FD DC = AB DC PMVS 2 10. 4 21 11. 20
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr mSPAT ÖRNEK 13 AB A B A A+B E E 12 F 16 BA DC D CF | | | |\"#$%ZBNVL [ AB ] // [ DC ] [ EF ] m [ BC ] ED = EA | | | |EF =CS BC =CS [AE a [DC = {F}PMBDBLõFLJMEF[EF]WF[CF] :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS ZJ¿J[FMJN && & 12.16 = 96 CS2EJS A^ EBC h = A^ ABE h = \"JTFFõпHFOMFSEFO A^ ECF h = A && A^ EDC h = B PMVSTB A^ ADE h = A +#PMVS :BOJ A^ ADE h = A^ ABCD h PMVS 2 2 \" \"#$% ==CS2CVMVOVS %m/*m A B E ÖRNEK 12 A 6B a h a DC E 6 h \"#$%ZBNVóVOEB [AB] // [DC] h D [AC] a [BD] = {E}PMNBLÐ[FSF 8 b && b A^ ADE h = A^ BEC hEJS 8C \"#$% EJL ZBNVL [AB] // [DC] [BE] m [EC] [ CE ] WF mSPAT | | | |[ BE ]B¿PSUBZ AB =CS DC =CS AxB & A^ ABD h = :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS x.h E den |#$|EJLJOEJSFMJN ²LMJEEFO E 2 h2 =PMEVôVOEBOI= 4 3 CSEJS h h & x.h A^ ABCD h = ^ 6 + 8 h.8 3 = 56 3 CS2CVMVOVS A^ BAC h = 2 2 DC && & A^ ABD h = A^ BAC h WF A^ AEB h PSUBL QBS¿B && PMEVóVOEBO A^ ADE h = A^ BEC hEJS 12. 56 3 22 13. 192
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 14 ÖRNEK 16 A B \"#$%ZBNVL ±óSFUNFOJ)BLBOhB[ AB ] // [ CD ]PMBDBLõFLJMEFCJS\"#$% 4 [AC] a [BD] = {E} yaNVóVOV¿J[NFTJOJJTUJZPS%BIBTPOSB\"%LFOBSÐ[FSJO- A A [AB] // [DC] EF CJS & OPLUBT #$ LFOBS Ð[FSJOEF CJS ' OPLUBTO BMQ E | | | |[ EF ]O¿J[NFTJOJJTUJZPS[EF] // [CD] AE = ED =CS & =CS2 % 3 br2 16 A^ AEB h m ( ADC ) = 60° A (ABCD) = 24 BMNBTO TËZMÐ- & h =CS2 ZPS4POPMBSBL&'V[VOMVóVOVCVMNBTOJTUJZPS A^ DEC DC #VOB HÌSF )BLBOhO WFSFDFôJ EPôSV DFWBQ LBÀ CJ- & SJNEJS :VLBSEBLJWFSJMFSFHÌSF A^ AED hLBÀCJSJNLBSFEJS A^ AED h = Aa & k = A A B BEC 4 \"2 =CS2 A^ & h =\"=CS2CVMVOVS E F AED 4 43 60° H C D4 \"EBOEJLJOEJSFMJN ÑÀHFOJOEFO A^ ABCD h = 24 3 = EF .4 3 |&'| =CSCVMVOVS ÖRNEK 15 ÖRNEK 17 39 6D 8 10 A 5B \"#$%ZBNVL .1 A a 6 [ AB ] // [ DC ] 3 k | |AD =CS E | |AB =CS 3 4 | |BC =CS | |DC =CS 66 3k D 5 10 K 5 C a a B 3C :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJNLBSF- \"#$%EJLZBNVL [AD] // [BC] [AB] m [BC], [ CE ]B¿PS- EJS | | | | | | | |UBZ AB = AE BC = 3CS AD =CS :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS \"%LFOBSOBQBSBMFMPMBDBLöFLJMEF[BK]EPôSVQBSÀBT- OÀJ[FMJN |%\"|WF|$&|ZJV[BUQ$EFO|\"%|ZFEJLJOEJSFMJN & 3.4 2 A^ ABCD h = ^ 9 + 3 h.8 = 48 CS2CVMVOVS A^ BKC h= 2 2 = 6 br EJS \" \"#$% =++=CS2CVMVOVS 14. 23 17.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 18 ÖRNEK 20 A B AF B \"#$%EJLZBNVL b a E 4 [EF] m [FG] D a a DC Hx [BC] m [DC] G | | | | | |\"#$%JLJ[LFOBSZBNVL AD = BC AC =CS b |AF| = |FB| |AE| = |ED| :VLBSEBLJWFSJMFSFHÌSF \" \"#$% nin FOCÑZÑL de- 4 | | | |BG = GC =CS ôFSJLBÀCJSJNLBSFEJS C A( ABCD ) =CS2 | |:VLBSEBLJWFSJMFSFHÌSF %$ =YLBÀCJSJNPMBCJ- MJS \" \"#$% FOCÑZÑLEFôFSJOJa =PMEVôVOEBBMS #'(WF()$CFO[FSÑÀHFOMFS x A^ ABCD h = 1 ·6.6 sin a = 1 ·6.6.sin90° =CS2 42 32 2 2 BF = 4 BF = x max CVMVOVS A^ ABCD h = d 64 +xn 8 = 80 x 2 64 + x2 x = 20 Y2 -Y+= 0 Y - Y -4 Y=WFZBY=PMVS ÖRNEK 19 ÖRNEK 21 #JSLBóEB[ AB ] // [ DC ]PMBDBLõFLJMEF\"#$%ZBNVóV- A 3B \"#$%ZBNVL [AB] // [DC] OV¿J[JOJ[#$LFOBSOOPSUBOPLUBTO&PMBSBLBMO[ a 5A b 4A 4A [ BD ] a [ AC ] = { F } % m | |AB =CS | |m(DAB) | |DC =CS < 90°, % = 2.m ( % ) AD =CS EG m ( DAE ) EAB | |AE =CSPMEVôVOBHÌSF \" \"#$% LBÀCJSJNLB- 4m 16A F 16A SFEJS 4b 4a 80A DC D 12 C a8 a :VLBSEBLJWFSJMFSFHÌSF ZBNVôVOBMBO \"&'ÑÀHF- 10 11 OJOJOBMBOOOLBÀLBUES 5E 2a 6 H & a A^ DFC h =\" EFSTFL B A && A^ DEF h = A^ FGC h =\" a 10 && A^ AEF h = A^ BFG h =\" K & & 11.8 = 44 CS2 A^ AFB h =\" A^ ADE h = 2 \" \"#$% =\"PMVS \" \"#$% = 2.44 =CS2CVMVOVS A^ ABCD h 125A 125 = = CVMVOVS & 4A 4 A^ AEF h 19. 24 125 20. 21. 4
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 22 ÖRNEK 24 D mC \"#$%ZBNVL Ax B \"#$%EJLZBNVL [AB] // [DC] A [AB] // [DC] [BD] a [AC] = {F} x [CE] a [BD] = {K} 6 E [AD] m [DC] F B 1K | |AD =CS | |AB =YCS | | | |4 AE = EB C C | |A 2k E k B FK =CS D x+4 | |KB =CS | |DC = (x + CS | |:VLBSEBLJWFSJMFSFHÌSF %' LBÀCJSJNEJS && :VLBSEBLJ WFSJMFSF HÌSF A^ DEC h - A^ AEB h GBSL LBÀCJSJNLBSFEJS %'$WF#'\"ÑÀHFOMFSJOEFCFO[FSMJLUFO && & mx A^ AEB h = A, A^ ADE h = B ve A^ DEC h = C PMTVO = 3k 5 %$,WF,&#ÑÀHFOMFSJOEFCFO[FSMJLUFO m x+1 x+1 x -\"+ B = 6.x = 3x =, = 2 k4 12 5 6^ x + 4 h Y=Y+ B +$= = 3x + 12 2 5 $-\"=CS2CVMVOVS x = CSCVMVOVS 7 ÖRNEK 23 ÖRNEK 25 \"#$%EJLZBNVL D 3 K3 C \"#$%ZBNVL A xB [ AE ] m [ ED ] 90°–a m % ) + % = 90° b % = % ( DAB m ( CBA ) a 90°–ax y m ( DAE ) m ( DEC ) E a 8 |DK| =|KC| 90°–a | |AD =CS 4 |AL| = |LB| a y C D aa bb | |DK =CS | | | |:VLBSEBLJWFSJMFSFHÌSF \"# . %$ ÀBSQNLBÀCJ- A 3 H x–3 L x.–3 M 3 B | |KL =CS SJNLBSFEJS | |:VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS x 88 %\"LFOBSOBQBSBMFMPMBDBLöFLJMEF[,)]OWF[#$]LFOB- 1JTBHPSUFPSFNJOEFO SOBQBSBMFMPMBDBLöFLMJEF[KM]OÀJ[FMJNa + b = 2 + Z-Y 2 = Y+Z 2 x+y PMEVôVOEBO m ( H%KM ) = 90°PMVS x y–x .VIUFöFNÑÀMÑEFO 64 + 2 - 2xy + 2 = 2 + 2xy + 2 Y- 3 = 4 jY=CSEJS y x x y |\"#| =Y=CSCVMVOVS YZ=jYZ= |\"#|. |%$| =YZ=CS2 CVMVOVS 5 23. 14 24. 12 22. 7
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 26 ÖRNEK 28 Dy C AB$%EJLZBNVL ôFLJM * EF LBMOMLMBS ËOFNTJ[ WF BSBMBSOEB DN a V[BLMLPMBOUBCBOBEJLWFCJSCJSJOFQBSBMFM¿VCVLMBSWF- B [ FE ] m [ BC ] SJMNJõUJS x b AE |BE| = |EC| = |FE| B F A A ( ABEF ) =CS2 a Bb y Ax B ADN DN | |:VLBSEBLJWFSJMFSFHÌSF \"% LBÀCJSJNEJS %'$WF#'\"FöÑÀHFOMFS \" \"#$% = ^ x + y h^ x + y h = 200 DN ôFLJM* 2 AD Y+Z 2 = 400 |\"%| =Y+Z=CSCVMVOVS ÖRNEK 27 150 150 B C 170 120 x K ôFLJM** ôFLJM*EFWFSJMFO\"#$пHFOJOEF(OPLUBTBóSMLNFS- ¥VCVLMBSOCPZMBSTSBTZMBDNWFDNEJS | | | |LF[JWF AB = GC EJSôFLJM*EFLJ\"($пHFOJLFTJ- 6[VO¿VCVLUBNPSUBTOEBOLSMZPSWFLSMBOQBS¿BOO BZBó EJóFSVDVLTB¿VCVLJMFBZOIJ[BZBHFMFDFLõF- MJQ[AC]CPZVODB\"#$пHFOJOFZBQõUSMBSBL\"#$%ZB- LJMEFLBZZPSWFôFLJM**PMVõVZPS NVóVFMEFFEJMJZPS #VOBHÌSF õFLJM**EFPMVöBO\"$#%EJLZBNVôVOVO BMBOLBÀDN2EJS A A 6D a a 6 GG 3a 0MVöBOEJLÑÀHFOEF 2 +Y2 = 1702 B CB 9 K9 C Y=DNEJS ôFLJM* ôFLJM** A^ ACBD h = d 200 + 120 n150 | |\"#$%ZBNVôVOEB[\"%] // [#$]WF \"% =CSPMEV- 2 | |ôVOBHÌSF #$ LBÀCJSJNEJS = 2400 \"($ÑÀHFOJOJ\"$LFOBSOBZBQöUSEôN[EBO m ( % ) = m ( % ) PMVS:BNVLUBQBSBMFMMJLUFO GAC DAC m ( % ) = m ( % ) PMVS|\"(| =CSJTF|GK| =CSPMVS ACB GAC \",$JLJ[LFOBSÑÀHFOPMEVôVOEBO|,$| =CSWF[\",] ke- OBSPSUBZPMEVôVOEBO|#$| =CSPMVS 20 27. 2400
:BNVL TEST - 7 1. DC \"#$%ZBNVL 4. A B A E [AB] // [DC] // KL // |AK| = |KC| 3 |DL| = |LB| | |AB = (2x + CS DC B | | | |\"#$%ZBNVL [DC] // [AB] AC = AD | |DC = (x + CS | |KL =CS m( % + % = 130° ADC ) m ( ABC ) | |:VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS :VLBSEBLJWFSJMFSFHÌSF m ( A%CB )LBÀEFSFDF- EJS \" # $ % & \" # $ % & 2. D C A 8 B A#$%ZBNVL [DC] // [AB] 6 E 2F 8 100° | |4 AB =CS | |BC =CS AB | |D 12 C DC =CS \"#$% ZBNVL [DC] // [AB] [ AE ] [ BF ] [ CF ] WF m % ) = 100° ( BAD | | | |[ DE ]B¿PSUBZ [EF] // [DC] AD =CS BC =CS | |EF =CS :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- | | | | :VLBSEBLJ WFSJMFSF HÌSF \"# + %$ UPQMBN BCD LBÀCJSJNEJS EJS \" # $ % & \" # $ % & 3. D C \"#$ пHFOJ õFLMJOEFLJ LBSUPOVO \",& пHFOJ JMF HËTUFSJMFO QBS¿BT [KE] CPZVODB LBUMBOEóOEB \" G3 E4 OPLUBT.OPLUBTOBHFMNFLUFEJS A [ AB ] m [ BC ] KE [ KE ] // [ BC ] AF B |AK| = 2|MB| | |BC =CS \"#$% ZBNVL [DC] // [AB] [AC] a [BD] = {G}, M | | | |[ AC ] a [ DF ] = { E } EG =CS CG =CS BC |BF| |= AF| | | \" ,#$& = CS2 PMEVôVOB HÌSF BM kBÀ | | :VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS CJSJNEJS \" # $ % & \" # $ % & 1. E 2. D 3. $ 27 4. $ \" \"
TEST - 8 :BNVL 1. D 7 C G 4. \"#$% ZBNVóV õFLMJOEFLJ LBSUPO [EF] CPZVODB 6F LBUMBOEóOEB\"WF#OPLUBMBSOOZFOJZFSMFSJTSB- TZMB\"hWF#hPMVZPS E 8 DC AB \"#$%ZBNVL [DC] // [AB] [ DE ]WF[ AG ]B¿PSUBZ EF | | | |[DG] a [AG] = {G} DE =CS AE =CS AB | |DC =CS | | :VLBSEBLJWFSJMFSFHÌSF $( LBÀCJSJNEJS | | | |3. #' = 2. '$ WF[\"#]JMF[%$]EPôSVQBSÀBMBS \" # $ % & BSBTOEBLJ V[BLML CS PMEVôVOB HÌSF [\"h#h] WF [%$] EPôSV QBSÀBMBS BSBTOEBLJ V[BLML LBÀ CJSJNEJS \" # $ % & 2. A B \"#$%ZBNVL [DC] // [AB] DC [DC] // [AB] [ HE ] // [ AB ] F [ AE ]WF[ DE ]B¿PSUBZ [ AC ] m [ BC ] 24 H E | |AD =CS | | | |E G | | | |AB + DC =CS BE = CE DC |AB| |= DC| A B m ( D%AC ) = 20° | | :VLBSEBLJWFSJMFSFHÌSF )& LBÀCJSJNEJS % :VLBSEBLJ WFSJMFSF HÌSF m ( CAE ) LBÀ EFSFDF- \" # $ % & EJS \" # $ % & | | | |3. AB > DC WF[ AB ] // [ DC ]PMBDBLõFLJMEFCJS | | | | AB > DC WF[ AB ] // [ DC ]PMBDBLõFLJMEFCJS \"#$% ZBNVóV ¿J[JOJ[ \"% LFOBSOO PSUB OPLUBT \"#$% ZBNVóV ¿J[JOJ[ %\" LFOBSOO Ð[FSJOEF CJS PMBDBLõFLJMEFCJS,OPLUBTCFMJSMFZJOJ[ ,OPLUBTWFZBNVóVOEõOEB$ZFEBIBZBLO$ | | | |[,$] m [$#] BK =CSWF #$ =CSPMEV- WF#JMFEPóSVTBMPMBDBLõFLJMEFCJS.OPLUBTBMQ ôVOBHÌSF CVZBNVôVOPSUBUBCBOOOV[VOMV- [ KM ]EPóSVQBS¿BTO¿J[JOJ[ ôVLBÀCJSJNEJS | | | | | |m(K%MB) = m(M%BA) AK = KD DC =CS | | | |AB =CSPMEVôVOBHÌSF KM LBÀCJSJNEJS A) 6 B) 2 10 C) 3 5 D) 73 E) 4 5 \" # $ % & 1. B 2. $ 3. D 4. \" $ D
:BNVL TEST - 9 1. A B 4. ,ËõFHFOMFSJEJLLFTJõFOCJSJLJ[LFOBSZBNVóVOUB- \"#$%ZBNVL CBOMBSCJSJNWFCJSJNEJS [DC] // [AB] #VOB HÌSF CV ZBNVôVO BMU WF ÑTU UBCBO BSB- TOEBLJV[BLMLLBÀCJSJNEJS | | | |AD = BC =BCS \" # $ % & | |AB =BCS | |D C CD =BCS :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- DAB EJS \" # $ % & | | | | | | | | AB > DC [ AB ] // [ DC ]WF AD = BC PMBDBL 2. A 5 B [DC] // [AB] õFLJMEFCJS \"#$%JLJ[LFOBSZBNVóV¿J[JOJ[ 6 D 11 C |AD| = |BC| [ AC ] a [ BD ] = {E }WF[ AC ] m [ BD ]PMBSBLBMO[ | |AB =CS %BIBTPOSB[ EB ]Ð[FSJOEFCJS,OPLUBTBMO[ | |BC =CS | |CD =CS | | | | | |[$,] // [%\"] \"# = 9 2 WF KB = 2. EK JTF | |DE LBÀCJSJNEJS \" # $ 3 3 D) 4 2 E) 4 3 :VLBSEBLJWFSJMFSFHÌSF m ( D%AB )LBÀEFSFDF- A B \"#$%ZBNVL EJS C D [DC] // [AB] \" # $ % & | |BC =CS | |AB =CS | |DC =CS | |AD =CS 3. A B [DC] // [AB] \"#$%ZBNVóV,` [DC]PMNBLÐ[FSF [BK]CPZVO- [ DB ] m[ AC ] DBLBUMBOEóOEBBõBóEBLJõFLJMFMEFFEJMJZPS | |DC =CS | | | |AD = BC = 2 17 CS C' A B L D 10 C DK | | :VLBSEBLJWFSJMFSFHÌSF \"# LBÀCJSJNEJS | | $h`\"#PMEVôVOBHÌSF -\" LBÀCJSJNEJS \" # $ % & A) 29 # $ 27 D) 24 20 7 E) 7 77 1. \" 2. $ 3. E 29 4. B $ $
TEST - 10 :BNVL 1. D C \"#$%EJLZBNVL | | | |4. AB > CD WF[ CD ] m [ DA ] [ BA ] m [ AD ]PMBDBL E [ BE ] [ CE ]B¿PSUBZ õFLJMEF\"#$%ZBNVóVOV¿J[JOJ[#%LËõFHFOJÐ[F- | |BC =CS SJOEFBMOBO,OPLUBTJ¿JO[ CK ] m [ BD ]EJS A ( ABCD ) =CS2 | | | | | |AD =CS AB =CS KC =CSPMEVóVOB | |HËSF BK LBÀCJSJNEJS AB \" # $ % & | | :VLBSEBLJWFSJMFSFHÌSF DE LBÀCJSJNEJS \" # $ % & 2. D C \"#$%EJLZBNVL ,-./ZBNVóVõFLMJOEFLJUBSMBOOFUSBGFõJLJ[LF- A [ AC ] m [ BC ] OBSZBNVLTBMCËMHFõFLMJOEF¿JNMFOEJSJMEJLUFOTPO- SB BSBEB LBMBO 1345 CËMHFTJ EF ZBNVL õFLMJOEF- | |AB =CS EJS | |DC =CS KL B PR NT SM | | :VLBSEBLJWFSJMFSFHÌSF \"% LBÀCJSJNEJS / JMF . OPLUBMBS BSBT V[BLML N PMEVôVOB HÌSF CBöMBOHÀUBUBSMBOOÀFWSFTJLBÀCJSJNEJS \" # $ % & \" # $ % & 3. D \"#$%EJLZBNVL D C \"#$%EJLZBNVL [ AC ] m [ BD ] E [ BE ] m[ EC ] | | | |C AE 2 + EB 2 =CS2 |DE| = |EA| | |DC =CS E | |AB =CS AB AB | | | | :VLBSEBLJ WFSJMFSF HÌSF \"% . #$ ÀBSQN | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS LBÀCJSJNLBSFEJS A) 12 B) 5 6 C) 4 10 \" # $ % & D) 6 5 E) 10 2 1. E 2. E 3. $ 30 4. D D \"
:BNVL TEST - 11 1. D 10 C [ DC ] // [ AB ] 4. D C [ DC ] // [ AB ] 8 | |BC =CS // E [ AC ] m [ BD ] A 6 // |AD| = |BC| | |DC =CS | |AB =CS | |A B CD =CS | |B AD =CS m ( D%AB ) + m % = 90° :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- ( CBA ) LBSFEJS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- \" # $ % & LBSFEJS \" # $ % & ôFLJMEFWFSJMFOEÐ[HÐOBMUHFOõFLMJOEFQFUFóJOCB- [OPLUBMBSCJSMFõUJSJMJQBõBóEBLJõFLJMFMEFFEJMJZPS 2. D C [ DC ] // [ AB ] [ CE ] // [ AD ] % = 30° m ( BAD ) | |E AB =CS %Ñ[HÑOBMUHFOöFLMJOEFLJQFUFLMFSJOCJSLFOBS | |DC =CS CSPMEVôVOBHÌSF PMVöBOöFLMJOBMBOLBÀCJ- SJNLBSFEJS | |A B AD =CS & :VLBSEBLJWFSJMFSFHÌSF A^ DEC hLBÀCJSJNLB- SFEJS A) 5 # $ % & 15 2 2 A) 1140 3 B) 1200 3 C) 1250 3 D) 1450 3 E) 1500 3 D4 C [ DC ] // [ AB ] 3. D C [ DC ] // [ AB ] 6 [ AE ] m [ DE] E A | |AB =CS |BE| = |EC| | | | |AD = BC =CS | |DC =CS | |CD =CS | | | |AB = DE =CS B :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- A 6B LBSFEJS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- \" # $ % & LBSFEJS \" # $ % & 1. \" 2. \" 3. $ 31 4. $ E E
TEST - 12 :BNVL 1. A B \"#$%ZBNVL 4. A B \"#$%EJLZBNVL E | | | | AB = DC E [ CE ]B¿PSUBZ A^ & h =CS2 | | | |AE = DE =CS BEC | |BC =CS DC DC :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS LBSFEJS \" # $ % & \" # $ % & DC 2. 14 E G A B \"#$%EJLZBNVL 3 F D [ AE ]WF[ DE ]B¿PSUBZ 6 E [ EF ] m [ AD ] A FB |AD| |= AF| \"#$%EJLZBNVL [ AE ]WF[ DE ]B¿PSUBZ | |BC =CS | |[ EG ] m [ BC ] [ EF ] m [ AF ] AD =CS C | | | |EG =CS EF =CSEJS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS LBSFEJS \" # $ % & \" # $ % & 3. D C E D C \"#$%ZBNVL A FB E |AE | = |DE| |AB| |= DC| | | | | | | | | | |\"#$%ZBNVL EC = EB AF = FB = DC AB :VLBSEBLJ WFSJMFSF HÌSF A (ABCD) PSBO A (ABCD) Taral› Alan :VLBSEBLJWFSJMFSFHÌSF PSBOLBÀ- US A (ABE) LBÀUS 9 D) 11 E) 6 A) 2 B) 59 E) 5 B) C) 3 D) \" C) 5 22 22 1. $ 2. D 3. \" 32 4. E E B
:BNVL TEST - 13 | | | |1. AB > DC WF[ AB ] // [ DC ]PMBDBLõFLJMEFCJS 4. \"#$% QBSBMFMLFOBS õFLMJOEFLJ LVNBõ QBS¿BT N \"#$%ZBNVóVOV¿J[JOJ[\"%WF#$LFOBSMBSÐ[F- EPóSVTV CPZVODB LFTJMJQ õFLJM ** EFLJ HJCJ CJSCJSJOF SJOEFTSBTZMB&WF'OPLUBMBSBMO[[EF] // [AB] EJLJMJZPS | | | |AB = DC =CS \" \"#'& =\" %&'$ N B | | PMEVôVOBHÌSF &' LBÀCJSJNEJS AE A) 3 2 B) 2 5 C) 21 D) 2 8 E) 5 D FC ôFLJM* | | | | | |F' D' EB = DF = AE 2. D 3 C [ DC ] // [ AB ] 3 | | | |AD = DC =CS E E' B A8 | |AB =CS B %% m ( DAB ) = 2.m ( CBA ) FC :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJN- ôFLJM** LBSFEJS A^ FCD'F'E'E h :VLBSEBLJWFSJMFSFHÌSF PSBO A) 10 2 B) 11 2 C) 12 2 A^ BD'F'E' h LBÀUS D) 14 2 E) 16 2 A) 8 B) 7 C) 2 D) 5 E) 4 3 3 33 AF B | | | |3. [ BA ] m [ AD ] [ AD ] m [ DC ]WF AB > DC PMB- EH DBLõFLJMEFCJS\"#$%ZBNVóVOV¿J[JOJ[\"%LFOBS Ð[FSJOEFCJS,OPLUBTBMO[ % CBA % D GC | | | | | |m(CKD) \"#$% ZBNVL [ AB ] // [ DC ] WF \" \"%& = CS2 = m ( ) DK = 2. ,\" #$ =CS A ( BHC ) =CS2EJS | |,$ = CS PMEVôVOB HÌSF \" \"#$% LBÀ CJ- :VLBSEBLJWFSJMFSFHÌSF \" &')( LBÀCJSJNLB- SJNLBSFEJS SFEJS A) 108 B) 106 C) 21 5 5 & % \" # $ % & 1. $ 2. B 3. \" 33 4. $ D
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr 1\"3\"-&-,&/\"3 TANIM ÖRNEK 2 ,BSõMLMLFOBSMBSCJSCJSJOFQBSBMFMPMBOEËSUHF- Dx E 5 F xC \"#$%QBSBMFMLFOBS ne QBSBMFMLFOBSEFOJS ba [ AF ] a [ BE ] = { G } %m/*m x+5 G x+5 [ AF ]WF[ BE ]B¿PSUBZ D C a b | |EF =CS a b | |AB =CS A B :VLBSEBLJWFSJMFSFHÌSF ¦ \"#$% LBÀCJSJNEJS A B ÷ÀUFSTBÀMBSEBOJLJ[LFOBSÑÀHFOMFSPMVöVS Y+= 9 \"#$%QBSBMFMLFOBS Y=CS ¦ \"#$% = + =CSCVMVOVS |AB| = |DC| |AD| = |BC| ÖRNEK 3 r m (WA ) = m (XC ) D 6 EC \"#$%QBSBMFMLFOBS r m (XD ) = m (WB ) 120° 30° 60° r m (WA ) + m (XD ) = 180° 6 [ AE ]B¿PSUBZ r m (XD ) + m (XC ) = 180° 6 B % = 30° m( DCB ) 60° 30° D C | |BC =CS A /E // // / | |:VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS AB ÷ÀUFSTBÀMBSEBOJLJ[LFOBSÑÀHFOMFSPMVöVS [AC] a [BD] = {E} [\"&] BÀPSUBZ PMEVôVOEBO m ( D%AE ) = m ( E%AB ) = 30° r |AE| = |EC| PMVS0IBMEF\"%&ÑÀHFOJOEF ÑÀHFOJOEFO r |DE| = |EB| |\"&| = 6 3 CSCVMVOVS ÖRNEK 1 %m/*m C |AE| = |EB| N |FB| = |FC| D B D F E C \"#$%QBSBMFMLFOBS K / / |DE| = |EC| |EC| = |BC| // // A EB A KB :VLBSEBLJWFSJMFSFHÌSF m ( A%EB )LBÀEFSFDFEJS [ AC] a [ DE ] = { K} [ KC] a [ DF ] = { N}JTF %\"LFOBSOBQBSBMFMPMBDBLöFLJMEF[EK]OÀJ[FSTFL | | | | | |KA = KN = NC PMVS |EK| = |\",|= |KB|PMVS | | | |C D / F/ C AE = EB 0IBMEFm ( A%EB ) = 90°PMVS | | | |N // CF = FD K // B // // AE | | | | | | PMEVóVOBHËSF AK = KN = NC EJS 1. 34 2. 32 3. 6 3
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 4 ÖRNEK 6 A B \"#%&QBSBMFMLFOBS G \"#$%QBSBMFMLFOBS 2 G |BC| = |CD| D F [ AF] a [ DB ] = { E} 4 C [ AG] a [ DC ] = { F} E H C |EF| = |FD| | |EF =CS | |EH = (2x + CS | |FG =CS | |E FD GB = (x + CS AB | |:VLBSEBLJWFSJMFSFHÌSF () LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS |#$| = |$%|WF|&'| = |'%|PMEVôVOEBO |\"&|2 == 24 |&)| = |)(| = |BG|PMVS |\"&| = 2 6 CSCVMVOVS Y+ 1 =Y+jY=CS |)(| =Y+=CSPMVS ÖRNEK 7 ÖRNEK 5 A 5a B \"#$%QBSBMFMLFOBS a DE C \"#$%QBSBMFMLFOBS a 5k [ BE ]B¿PSUBZ D2 E F a [ AC ] m [ BC ] [ EF ] // [ AD ] 3k 3a | | | | AC = FC | |AF =CS | |DE =CS 11 F | |BF =CS | |AD =CS 16 ab 12 3a C x b a a b A xK xB :VLBSEBLJWFSJMFSFHÌSF ¦ \"#$% LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS \"#$ÑÀHFOJOEFBÀPSUBZUFPSFNJOEFO [EK] #$WF\"%LFOBSOBQBSBMFMPMEVôVOEBO 3|\"#| =|#$|PMVS#$&JLJ[LFOBSÑÀHFOJOEF |#$| = |&$| =BPMVS % = m ( % ) WF m ( % ) = % ) PMVS m ( FAK ) AFK FBK m ( KFB B+ 2 =BjB= 1 ¦ \"#$% =B=BjB=CSCVMVOVS 0IBMEF |\",| = |KB| = |',| '\"#ÑÀHFOJOEFQJTBHPSCBôOUTOEBOY=CSPMVS Y=CS |&'| = 11 - 10 =CSCVMVOVS ÖRNEK 8 A 4 12° B \"#$%QBSBMFMLFOBS 12° 4 %m/*m [ AF] m [ DC ] E 4 4 24° 8 K D F m ( A%BD ) = 12° E C 24° | |AD =CS DF | |C BE =CS G :VLBSEBLJWFSJMFSFHÌSF m ( D%AB )LBÀEFSFDFEJS AB [\",]LFOBSPSUBZOÀJ[FSTFL |\"%| = |\",|PMVS \"#$%QBSBMFMLFOBS % + 36 = 180° m ( DAB ) [AE] a [ DC ] = {F} [AE] a [BD] = {G} m ( D%AB ) = 144°CVMVOVS | | | | | |AG 2 = GF GE EJS 4. 9 1 2 6 7.
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 9 %m/*m A B \"#$%QBSBMFMLFOBS D C x aa [ AF ]WF[ DF ]B¿PSUBZ M E 13–x 6 F [ FE] m [ DC ] b 6 b m ( D%AB ) > % A B d m ( ADC ) A' B' C' D' E' D 13–x E | |C FE =CS | |AD =CS | |:VLBSEBLJWFSJMFSFHÌSF DE LBÀCJSJNEJS \"#$%QBSBMFMLFOBS [\"\"h] mE [%%h] m d [&&h] mE [##h] mE [$$h] m d \"'WF'%BÀPSUBZPMEVôVOEBOm ( D%FA ) = 90°EJS ²LMJEUFPSFNJOEFO2 =Y -Y jY2 -Y+= 0 &LËõFHFOMFSJOLFTJNOPLUBT Y -4 | | | | | | | | | |\"\"h + $$h = ##h + %%h = &&h EJS Y-9 % Y=WFY= GBLBUm ( D%AB ) > m( ADC ) PMEVôVOEBO Y=UÑS0IBMEF|DE| = |DM| =PMVS %m/*m D C ÖRNEK 10 d C' A 5 E 5B \"#$%QBSBMFMLFOBS B' D' B % = 60° m ( ADC ) 4 44 4 | | | |AE = EB =CS A A' 60° | |BC =CS D5 60° K 4 F1 C | |CF =CS \"#$%QBSBMFMLFOBS [A\"h] mE [%%h] mE [##h] mE [$$h] m d | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS | | | | | | | |\"\"h + ##h + $$h = %%h EJS %\"LFOBSOBQBSBMFMPMBDBLöFLJMEF[EK]OÀJ[FMJN0IBMEF ÖRNEK 12 &,'ÑÀHFOJFöLFOBSÑÀHFOPMVS|&'|=CSPMVS D C ÖRNEK 11 E F \"#$%QBSBMFMLFOBS d A C' B [ KL] m [ DC ] AB D K D' LC [ KE] m [ DE ] A' | | | | KE = KL \"#$%QBSBMFMLFOBS [ \"\"h] mE [ %%h ] mE [ $$h ] m d | |DC =CS | | | |\"\"h =CS $$h =CS | |:VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS | |:VLBSEBLJWFSJMFSFHÌSF %%h LBÀCJSJNEJS \" \",% =\" %,$ PMBDBôOEBO|KL| = |%\"| . |EK| |\"\"h| + |$$h| = |%%h|PMEVôVOEBO 12· KL = DA |%\"| = 12· 3 =CS |%%h| = 4 + 3 |%%h| =CSCVMVOVS EK 4 |#$| =CSCVMVOVS 9. 9 10. 4 11. 9 12. 7
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 13 ÖRNEK 15 D 15 C \"#$%QBSBMFMLFOBS D 8 E 4C \"#$%QBSBMFMLFnar 8 a 120° 30° 60° 8 43 [ AE ]B¿PSUBZ a [ AE]WF[ CF ] 30° 8 30° % = 60° 8 B¿PSUBZ 30° B m ( DCB ) A 2a 7 a | |AE =CS A | |DE =CS | |B AD =CS 90°–a a F 8 | |DC =CS G 5 E :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS | |:VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS \"&BÀPSUBZPMEVôVOEBO m ( % ) = 30° PMVS DAE |%\"| = |DE|= |#$|=CS &#$ÑÀHFOJOEFLVSBMO- $'BÀPSUBZPMEVôVOEBO m ( % ) = m( % PMVS EBO|BE| = 4 3 WF[&$| =CSPMVS BCF BFC ) m ( % ) = 180° - 2a = 90° - a PMVS 0IBMEF A (ABCD) = 12.4 3 = 48 3 CS2CVMVOVS EAF 2 :BOJm ( A%EF ) = 90°PMVS0IBMEF|'&|2 +2 = 72 ÖRNEK 16 FE = 2 6 CSCVMVOVS E \"#$%QBSBMFMLFOBS ÖRNEK 14 3 4 B [ DF ]B¿PSUBZ A [ FE] m [ DE ] F 5 a [ FK] m [ DC ] D 8 C \"#$%QBSBMFMLFOBS 54 | |AE =CS 3 aa | |FE =CS [ AB] // [ EF ] a | |KC =CS a M6 3aE F 3 [ AE ] [ CF ] D 8 K 2C b 3 K6 [ DE ]WF[ BF ]B¿PSUBZ 3b | |3 :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS b AB =CS 8 | |B A BC =CS | |:VLBSEBLJWFSJMFSFHÌSF E' LBÀCJSJNEJS %'BÀPSUBZPMEVôVOEBOm ( A%DF ) = m ( A%FB ) EJS %&WF\"&BÀPSUBZPMEVôVOEBOm ( D%EA ) = 90°EJS$'WF :JOF%'BÀPSUBZPMEVôVOEBO |DE| = |DK| =CSEJS \" \"#$% = 10.4 =CS2 CVMVOVS #'BÀPSUBZPMEVôVOEBO m ( % ) = 90° EJS CFB |EM| = |MD| = |.\"| =CSWF|',| = |$,| = |KB| =CS %m/*m |&'| =-=CSCVMVOVS A B 1BSBMFMLFOBSEB\"MBO E ABCD %m/*m D QBSBMFMLFOBS [ AC ] WF [ BD ] C LËõFHFO A B [AC] a [BD] = {E} &&&& A^ AED h = A^ AEB h = A^ BEC h = A^ DEC hEJS a A E B ABCD QBSBMFMLFOBS DE C E ` [ AB ] % \"#$%QBSBMFMLFOBS m ( ADC ) = a [ AE ] m [ DC ] DC | | | |r A ( ABCD ) = DC AE & A (ABCD) | | | |r A ( ABCD ) = AD DC TJOa A^ DEC h = EJS 2 13. 2 6 14. 2 37 48 3 40
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 17 ÖRNEK 19 D E C DF E C ABCD 5 G x=12 paralelkenar a b 24 10 | |AG = 24 br a b | |BG = 10 br A B | |A B GF = 5 br ABCD paralelkenar, [ AE ] ve [ BE ]B¿PSUBZ [ BF ] a [ AE ] = { G }, [ AE ] ve [ BF ]B¿PSUBZ | | | |AB = 10 br, BE = 6 br :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS \"&WF#'BÀPSUBZPMEVôVOEBO m ( % ) = 90° AGB [\"&]WF[#&]BÀPSUBZPMEVôVOEBO m^ % h = 90° PMVS 24 10 AEB #FO[FSMJLUFO x = 5 Y=CS \"&#ÑÀHFOJOEFQJTBHPSUFPSFNJOEFO A^ ABE h = 36.10 = 180 \" \"#$% = 180.2 =CS2CV- 2 62 + |\"&|2 = 102 MVOVS |\"&| =CS A^ AEB h = 6.8 2 2 = 24 br ÖRNEK 20 \" \"#$% =\" \"&# =CS2CVMVOVS DM C ABCD paralelkenar F A 8 [ EF ] // [ DC ] L [ KM ] // [ DA ] A E A ( AKLE ) = 8 br2 8B B AK B :VLBSEBLJWFSJMFSFHÌSF \" .-'$ LBÀCJSJNLBSFEJS ÖRNEK 18 Dk E 2k C ABCD paralelkenar && %&-.QBSBMFMLFOBSOEB A^ DEL h = A^ DML h #,-'QBSB- 2a 4A 2m 2.|DE| = |EC| 11A F 6A && 3m 9A 3a A ( ADEF ) = 33 br2 MFMLFOBSOEB A^ LKB h = A^ BLF h WF \"#$% QBSBMFMLFOB- SOEB Aa & k = A^ & h = EJS \" .-'$ = 8 CS2 CV- DBC DAB MVOVS A 3k B & :VLBSEBLJWFSJMFSFHÌSF A^ BFC hLBÀCJSJNLBSFEJS &$'WF\"'#ÑÀHFOMFSJOEFCFO[FSMJLUFO %m/*m && A B E 3 |&'| = 2|'#|PMVS0IBMEF 2 A ^ FCB h = 3 A ^ FEC hWF && 2A ^ AFB h = 3A ^ FBC hEJS\" \"%&' =\"-\"=\" \"= 33 j\"= 3 A^ & h =\"=CS2CVMVOVS BFC DC \"#$%QBSBMFMLFOBS &QBSBMFMLFOBSOJ¿CËMHF- TJOEFIFSIBOHJCJSOPLUB && && A^ AEB h + A^ DEC h = A^ ADE h + A^ BEC hEJS 17. 48 18. 18 38 19. 360 20. 8
www.aydinyayinlari.com.tr ÇOKGENLER VE DÖRTGENLER 3. MODÜL ·/÷7&34÷5&:&)\";*3-*, ÖRNEK 21 ÖRNEK 22 D C D 2a C k E K A L k F k 3A AB AA // // A a Ea B \"#$%QBSBMFMLFOBS \" \"#$% =CS2 A^ & h =CS2 | | | | | | | |\"#$%QBSBMFMLFOBS AE = EB BF = FC AEB A ( KLBF ) =CS2 & :VLBSEBLJWFSJMFSFHÌSF A^ DEC hLBÀCJSJNLBSFEJS :VLBSEBLJWFSJMFSFHÌSF \" \"#$% LBÀCJSJNLBSFEJS && && $-#ÑÀHFOJOEF5IBMFTUFPSFNJOEFO A^ AEB h + A^ DEC h = A^ DAE h + A^ ECB h \" ,-#' =\" $,' EJS \"= 42 j\"= 14 0 IBMEF \"&# WF %&$ ÑÀHFOMFSJOJO BMBOMBS UPQMBN UÑN \" \"#$% =\"=\" BMBOOZBSTES \" \"#$% = 12.14 =CS2 CVMVOVS & + A^ DEC h= 14 A^ DEC h =CS2CVMVOVS %m/*m A B ÖRNEK 23 F B H 4 D G / A // F / 5 AA E E // C DC \"#$%QBSBMFMLFOBS \"#$%QBSBMFMLFOBS A^ & h =CS2 A^ & h =CS2 ADF FEB [AE] a [BD] = {G} [AF] a [BD] = {H} & :VLBSEBLJWFSJMFSFHÌSF A^ DEC hLBÀCJSJNLBSFEJS | | | | | | | |DE = EC BF = FC JTF %'#$ZBNVôVOEB & & & A (ABCD) && r A^ ADG h = A^ AGH h = A^ AHB h = A^ DFE h = A^ BEC h=\"PMTVO 6 A^ & h = & hPMEVôVOEB A^ & h =CS2PMVS ABD A^ BDC DEC r & = & = A (ABCD) A(DGE) A(HBF) 12 r & = A (ABCD) EJS A(EFC) 8 21. 39 22. 23. 9
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr ÖRNEK 24 ÖRNEK 26 \"#$% QBSBMFMLFOBS õFLMJOEFLJ LBSUPO [AC] LËõFHFOJ \"#$%QBSBMFMLFOBSO ¿J[JQ #WF$JMFEPóSVTBMPMBDBL õFLJMEF QBSBMFMLFOBSO EõOEB CJS - OPLUBT JõBSFUMFOJ- CPZVODBLBUMBOZPSWFõFLJM**EFLJLBSUPOPMVõVZPS ZPS A 10 D [ AL ] a [ DC ] = { K}WF[ AL ] a [ DB ] = { E }PMBDBLõF- 6 LJMEF&WF,OPLUBMBSCFMJSMFOJZPS | | | |AE =CS KL =CSWF\" &#$, =CS2 PMEVôV- OBHÌSF \" \"#$% LBÀCJSJNLBSFEJS B C ôFLJM* AB 2 4A 2n 2A E 5A A 10 D n a k b A1 aa a 6 DK C 5 x 6 M 10–x . 3 BE K 2a 5 a a x b T . L C |\"&| 2 = | EK | | EK | + 6 4 = | EK | | EK | + WF| EK | =CS D' \"=CS2 j\"=CS2 ôFLJM** \" \"#$% =\"=CS2CVMVOVS | | | |[\"%h]BÀPSUBZ \"# =CS \"% =CSPMEVôVOB | |HÌSF &$ LBÀCJSJNEJS ÖRNEK 25 \",%WF%$.ÑÀHFOMFSJCFO[FSMJôJOEFO DE 15k . 65 25 5k F = k= C 10 k 3 0IBMEF|\"5| = 50 PMVS 3 |\"$| = |\"5| - h |\"$| = 50 32 -= CS 33 A G 3k H B [\"&]BÀPSUBZPMEVôVOEBO | | | | | | | |\"#$%QBSBMFMLFOBS DC = EF AB = GH 32 A ( ABCD ) =CS2 36 :VLBSEBLJWFSJMFSFHÌSF \" ()'& LBÀCJSJNLBSFEJS = x 10 - x 32 x = CSCVMVOVS 5 \" \"#$% = |%$| . h =LIj kh =CS2 ^ 3k + 5k hh 2 \" ()'& = = 4k h = 16 br CVMVOVS 2 24. 40 32 5
1BSBMFMLFOBS TEST - 14 1. A B 4. D C EF F DC A EB | | | |\"#$%QBSBMFMLFOBS AB= AC m ( % ) = 40° | | | | | |\"#$%QBSBMFMLFOBS AE = EB = BC CAB % % = 20° m ( ACE ) = 20° m ( FDC ) :VLBSEBLJWFSJMFSFHÌSF m ( D%FA )LBÀEFSFDFEJS :VLBSEBLJ WFSJMFSF HÌSF m ( D%FC ) LBÀ EFSFDF- \" # $ % & EJS \" # $ % & 2. D C E D C A BE AB | | | |\"#$%QBSBMFMLFOBS BC = BE \"#$%QBSBMFMLFOBS [ AD ]WF[ BE ]B¿PSUBZ % = 130° m ( A%EB ) = 60° m ( DCE ) :VLBSEBLJ WFSJMFSF HÌSF m ( % ) LBÀ EFSFDF- :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS DAB DCB EJS \" # $ % & \" # $ % & 3. D E C F A B AB E 190° | | | |\"#$%QBSBMFMLFOBS BF = BC [ AE ] m [ DC ] DC % = 30° | | | | | | | |\"#$%QBSBMFMLFOBS AE = BE DE = BC m ( DAE ) m ( D%CB ) = 110° m ( D%EB ) = 190° :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS :VLBSEBLJWFSJMFSFHÌSF m ( A%BE )LBÀEFSFDFEJS DBA \" # $ % & \" # $ % & 1. D 2. E 3. $ 41 4. \" B D
TEST - 15 1BSBMFMLFOBS 1. D C 4. D C F G E E F AB AB \"#$%QBSBMFMLFOBS [ DE ]WF[ CE ]B¿PSUBZ \"#$%QBSBMFMLFOBS [ AC ] a [ BD ] = { G} | |[ EF ] // [ AB ] EF =CS ¥ \"#$% =CS | | :VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS | | | | | |BF = CF GE =CS | |:VLBSEBLJWFSJMFSFHÌSF BD LBÀEFSFDFEJS \" # $ % & \" # $ % & D C 2. D C E F E A BG A BF | | | |\"#$%QBSBMFMLFOBS EF = DE | |\"#$%QBSBMFMLFOBS [BC] a [DF] = {E} DF =CS | |[ AC ] a [ DG ] = { E } DC =CS | | | |AB = BF ¥FWre ( ADF ) =CS | | :VLBSEBLJWFSJMFSFHÌSF BG LBÀCJSJNEJS | | | | :VLBSEBLJ WFSJMFSF HÌSF BE + #' UPQMBN \" # $ % & LBÀCJSJNEJS NEPóSVTV\"#$%QBSBMFMLFOBSOFõJUBMBOMJLJCËM- \" # $ % & HFZFBZSZPS AD G FN E 3. D FC BC E #VOBHÌSF AB * | AE| = | FC| | | | |** FC = BE \"#$%QBSBMFMLFOBS [ AG ] a [ BD ] = { E} *** NEPóSVTVQBSBMFMLFOBSOBóSMLNFSLF[JOEFO | | | | # $WF(EPóSVTBM EF =CS EG =CS | | :VLBSEBLJWFSJMFSFHÌSF \"& LBÀCJSJNEJS HF¿FS WFSJMFSJOEFOIBOHJMFSJLFTJOMJLMFEPôSVEVS A) 2 3 B) 3 3 C) 4 3 \" :BMO[* # :BMO[** $ * *** D) 6 E) 8 % ** *** & * ** *** 1. $ 2. $ 3. $ 42 4. B \" $
1BSBMFMLFOBS TEST - 16 1. E ABCD 4. D EF C ABCD QBSBMFMLFOBS QBSBMFMLFOBS A A D [ DE ] m [ BE ] G [GF] // [AD] [ AF ] m [ BD ] | |AB =CS | |F DE =CS | |B DE =CS | |DC =CS | | :VLBSEBLJWFSJMFSFHÌSF $' LBÀCJSJNEJS | |B C BD =CS A) 1 B) 3 C) 2 D) 3 E) 7 22 | | :VLBSEBLJWFSJMFSFHÌSF \"' LBÀCJSJNEJS \" # $ % & 2. \"#$%QBSBMFMLFOBSOEB\"#,пHFOJ[ BK ]CPZVODB D C LBUMBOEóOEB\"OPLUBT&OPLUBTJMF¿BLõZPS DE C 45° E K AF B A 12 B ABCD QBSBMFMLFOBS [ DF ] m [ AB ] [ DE ] m [ BC ] % | | | | | | EC = AF AD =CS DEK | | :VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS | |ma k = 45° \"# =CSWF | | | | | |EK + KD = 8 2 CSPMEVôVOBHÌSF $& LBÀ \" # $ % & CSEJS A) 6 3 B)4 6 C) 3 10 D) 2 21 E) 4 5 3. A B ABCD A B ABCD QBSBMFMLFOBS QBSBMFMLFOBS | |E AE =CS F G |DE| = |EC| | |DE =CS D EC |CG| = |BG| | |D C | |AE =CS AB = 2 13 CS | | :VLBSEBLJWFSJMFSFHÌSF '& LBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS \" # $ % & \" # $ % & 1. B 2. E 3. $ 43 4. D D \"
TEST - 17 1BSBMFMLFOBS 1. A B 4. K E A M B DC DC \"#$%QBSBMFMLFOBS . QBSBMFMLFOBSOBóSMLNFS- ABCD QBSBMFMLFOBS [ DE ]WF[ CE ]B¿PSUBZ | | | |LF[J [ DK ] m [ KB ] KM =CS KB =CS | | | |DE =CS CE =CS | | :VLBSEBLJWFSJMFSFHÌSF KD LBÀCJSJNEJS :VLBSEBLJWFSJMFSFHÌSF \"OPLUBTOO#$EPô- \" # $ % & SVTVOBFOLTBV[BLMôLBÀCJSJNEJS \" # $ % & 2. A B F AK B D EC DC \"#$% QBSBMFMLFOBS [ FE ] m [ DC ] [AF] WF [BF] | | | |\"#$%QBSBMFMLFOBS DK =CS KC =CS |AK| = |KB| = |AD| | | | | | |B¿PSUBZ DE =CS EC =CS FE =CS | | :VLBSEBLJWFSJMFSFHÌSF %$ LBÀCJSJNEJS | | :VLBSEBLJWFSJMFSFHÌSF #$ LBÀCJSJNEJS \" # $ % & \" # $ % & 3. A B 8 #JS LBóEB CJS \"#$% QBSBMFMLFOBSO ¿J[JOJ[ %$ K LFOBSÐ[FSJOEF [ DK ] m[ KB ]PMBDBLõFLJMEFCJS, DC OPLUBT BMO[ \"$ LËõFHFOJOJO PSUB OPLUBTO . PMBSBLBMO[ | | | |\"#$%QBSBMFMLFOBS [ AK ] m[ AD ] DK = KB | |AB =CS | | | | | |DK 2 + BK 2 =CS2PMEVôVOBHÌSF KM | | :VLBSEBLJWFSJMFSFHÌSF \", LBÀCJSJNEJS LBÀCJSJNEJS \" # $ % & \" # $ % & 1. B 2. \" 3. $ 44 4. \" B B
1BSBMFMLFOBS TEST - 18 1. D C 4. A F B G E E F B DC A ABCD QBSBMFMLFOBS [ DE ]WF[ CE ]B¿PSUBZ \"#$%QBSBMFMLFOBS [ AC ] a [ BD ] = { E} % ABC | | | | | | | |AF = FE GE = DG \" \"%(' =CS2 | |[ EF ] [ m AB ] m ( ) = 60° EF =CS :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS A^ DEC h = 6 3 br2 \" # $ % & :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS A) 18 3 B) 20 3 C) 24 3 D) 25 3 E) 28 3 2. F A G B DE C F AB D EC \"#$%QBSBMFMLFOBS [ AF ] a [ BF ] = { F} | | | |\"#$%QBSBMFMLFOBS AG =CS GB =CS | |EC =CS \" \"('% + A ( BFEC ) =CS2 | | | |EC = DE \" \"#$% =CS2 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- & LBSFEJS :VLBSEBLJWFSJMFSFHÌSF A^ FDE hLBÀCJSJNLB- \" # $ % & SFEJS \" # $ % & \"#$% QBSBMFMLFOBS õFLMJOEFLJ LBSUPO [ AE ] WF [ GH ]CPZVODBLFTJMJQ[DE]WF[BG]CPZVODBLBUMB- OZPS A HB 3. D C E K G F AE B D FC \"#$%QBSBMFMLFOBS [ BD ] a [ CE ] = { F} 1BSBMFMLFOBSOBMBOCJSJNLBSFWF\"&'$,() CÌMHFTJOJO BMBO CJSJNLBSF PMEVôVOB HÌSF | | | |AE = EB \" \"#$% =L\" $'# \"&% WF )#( ÑÀHFOMFSJOJO BMBOMBS UPQMBN LBÀ CJSJNLBSFEJS :VLBSEBLJWFSJMFSFHÌSF LLBÀUS \" # $ % & \" # $ % & 1. D 2. \" 3. \" 4. E B B
TEST - 19 1BSBMFMLFOBS 1. A B 4. A B E G E F DC DC | |\"#$%QBSBMFMLFOBS BC =CS \"#$%QBSBMFMLFOBS \" \"#$% =CS2 && & && A ^ GEF h = A ^ DFC h + A ^ EAB h 3.A ^ DEC h = 4.A ^ AEB h & | | :VLBSEBLJWFSJMFSFHÌSF &' LBÀCJSJNEJS :VLBSEBLJWFSJMFSFHÌSF A ^ AEB hLBÀCJSJNLB- \" # $ % & SFEJS \" # $ % & A B E 2. A HG B DC \"#$%QBSBMFMLFOBS [ DE ]B¿PSUBZ [ AE ] m [ DE ] A^ & =CS2 DEC h DE FC :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- LBSFEJS | | | |\"#$%QBSBMFMLFOBS AB = HG | | | | DC = EF \" \"#$% =L\" )('& \" # $ % & :VLBSEBLJWFSJMFSFHÌSF LLBÀUS A) 40 B) 40 C) 40 D) 40 E) 40 \"#$%QBSBMFMLFOBSõFLMJOEFLJUBSMBOO,CËMHFTJ- 17 13 11 9 7 OFLB[L¿BLMQQBSBMFMLFOBSOLËõFMFSJOFJQMFS¿F- LJMJQõFLJMEFLJCËMHFMFSFMEFFEJMJZPS 3. A B F %BIBTPOSB\"%,CËMHFTJOFCVóEBZ#,$CËMHFTJOF D EC BSQB FLJMJZPS ,B[L ¿BLMBO OPLUBOO \"% LFOBSOB PMBO V[BLMó #$ LFOBSOB PMBO V[BLMóOO LBU- \"#$%QBSBMFMLFOBS [ AE ] m [ BF ] ES | |AE =CS A ( ABCD ) =CS2 5ÑNUBSMBOOBMBON2PMEVôVOBHÌSF CVô- | | :VLBSEBLJWFSJMFSFHÌSF #' LBÀCJSJNEJS EBZFLJMFOBMBO BSQBFLJMFOBMBOEBOLBÀN2GB[- MBES \" # $ % & \" # $ % & 1. $ 2. \" 3. D 4. B $ $
1BSBMFMLFOBS TEST - 20 1. D C 4. ôFLJMEFWFSJMFO\"#$%QBSBMFMLFOBSõFLMJOEFLJUBS- 60° MBOO % OPLUBTOEBO \"# LFOBSOO PSUB OPLUBTOB F4 CJSJQHFSJMJZPS E A K B 3 A GB N \"#$%QBSBMFMLFOBS & \"#$%QBSBMFMLFOBSOBóSML NFSLF[J [EF] m [AD] [EG] m [AB] m ( % ) = 60° DC DCB | | | |EF =CS EG =CS :JOF \" OPLUBTOEBO #$ LFOBSOO PSUB OPLUBTOB CJS JQ HFSJMJZPS öQMFSJO LFTJN OPLUBMBS . JMF JTJN- :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- MFOEJSJMJZPS %BIB TPOSB \"%. CËMHFTJOF TBMBUBML LBSFEJS .,#/CËMHFTJOFEPNBUFTFLJMJZPS A) 16 3 B) 24 3 C) 32 3 #VOBHÌSF EPNBUFTFLJMFOBMBO TBMBUBMLFLJMFO BMBOOLBÀLBUES D) 40 3 E) 48 3 1 13 A) B) C) 1 D) E) 2 2. A 3 22 GB A B FE D EC F C \"#$%QBSBMFMLFOBS [ AE ] a [ DG ] = { F} DH & =CS2 G A^ ADF h | | | |AG GB & h =CS2 \"#$%WF#&('QBSBMFMLFOBS A^ ABE A ( BEFG ) =CS2 & =CS2 A^ & =CS2 :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- A^ DEH h HGC h LBSFEJS & :VLBSEBLJ WFSJMFSF HÌSF A^ BCF h LBÀ CJSJNLBSF- \" # $ % & EJS \" # $ % & 3. A G B A B F H E K M DE C | | | | | | | |\"#$%QBSBMFMLFOBS AF DF EC DE DG C & & & =CS2 ^ DFE h ^ GEC \"#$%QBSBMFMLFOBS A^ BKC h A + A h =CS2EJS A ^ & h =CS2 A^ & h =CS2 EHM AHB :VLBSEBLJ WFSJMFSF HÌSF \" \"#$% LBÀ CJSJN- & LBSFEJS :VLBSEBLJWFSJMFSFHÌSF A^ MGK h kBÀCJSJNLB- SFEJS \" # $ % & \" # $ % & 1. $ 2. D 3. \" 47 4. $ B $
·/÷7&34÷5&:&)\";*3-*, 3. MODÜL ÇOKGENLER VE DÖRTGENLER www.aydinyayinlari.com.tr &õ,&/\"3%²35(&/ TANIM ÖRNEK 2 ,BSõMLMLFOBSMBSQBSBMFMWFUÐNLFOBSMBSFõJU E \"#$% FõLFOBS EËSU- PMBOEËSUHFOFFöLFOBSEÌSUHFOEFOJS HFO // A B // 30° 120° [ AE ] m [ EC ] // // |AE| = |EC| %m/*m 15° % 30° m ( BCE ) = 15° A // B DC :VLBSEBLJWFSJMFSFHÌSF m ( A%DC )LBÀEFSFDFEJS E |\"&| = |&$|PMEVôVOEBOm(A%CE ) = 45°EJS D // C 0IBMEFm ( B%CA ) = 30°WF \"#$%FõLFOBSEËSUHFOJTF % r[ BD ] m [ AC ] m ( ADC ) = CVMVOVS r[ AC ]WF[ BD ]B¿PSUBZ | | | | | | | | r AE = EC WF DE = BE EJS NOT: &õLFOBSEÌSUHFO QBSBMFMLFOBSOCÑUÑOÌ[FM- MJLMFSJOJTBôMBS ÖRNEK 1 ÖRNEK 3 B B A aa 2a \"#$%FõLFOBSEËSUHFO E 55° |AE| = |BE| = |BD| F Aa C 35° 35° 2a 20° E D CG 2a \"#$%FõLFOBSEËSUHFO <\"(>m<#$> m ( % ) = 20° AGD D :VLBSEBLJWFSJMFSFHÌSF m ( % ) LBÀEFSFDFEJS :VLBSEBLJWFSJMFSFHÌSF m ( A%BC )LBÀEFSFDFEJS AED #&%ÑÀHFOJOEF [BD]BÀPSUBZPMEVôVOEBO m ( % ) = m ( % ) = 35° ADB BDG a = EJS a = % % = 20° + 35° = 55° CVMVOVS m ( AED ) m ( ABC ) = 4a = 144°CVMVOVS 1. 144 2. 3.
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